%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.11", %%% date = "16 March 2019", %%% time = "10:17:43 MDT", %%% filename = "ecp.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~beebe", %%% checksum = "27285 31847 150691 1440908", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; BibTeX; Electronic %%% Communications in Probability", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a COMPLETE bibliography of %%% publications in the open-source journal, %%% Electronic Communications in Probability %%% (CODEN none, ISSN 1083-589X, ISSN-L %%% 1083-589X) published in collaboration with %%% the Institute of Mathematical Statistics. %%% Publication began at the University of %%% Washington (Seattle, WA, USA) with volume 1, %%% number 1, in 1996. There is only one volume %%% per year, but articles are available online %%% as soon as they have been accepted for %%% publication. %%% %%% In 2016, journal hosting moved to Project %%% Euclid. %%% %%% The journal has Web sites at %%% %%% https://projecteuclid.org/euclid.ecp %%% http://ecp.ejpecp.org/ %%% http://www.math.washington.edu/~ejpecp/ECP/ %%% %%% There is also a companion journal for longer %%% articles; it is covered in ejp.bib. %%% %%% At version 1.11, the year coverage looked %%% like this: %%% %%% 1996 ( 10) 2004 ( 20) 2012 ( 63) %%% 1997 ( 8) 2005 ( 30) 2013 ( 96) %%% 1998 ( 13) 2006 ( 34) 2014 ( 87) %%% 1999 ( 17) 2007 ( 46) 2015 ( 95) %%% 2000 ( 14) 2008 ( 59) 2016 ( 76) %%% 2001 ( 15) 2009 ( 57) 2017 ( 60) %%% 2002 ( 19) 2010 ( 51) 2018 ( 93) %%% 2003 ( 21) 2011 ( 70) 2019 ( 11) %%% %%% Article: 1065 %%% %%% Total entries: 1065 %%% %%% Data for this bibliography have been derived %%% primarily from data at the publisher Web %%% site, with contributions from the BibNet %%% Project and TeX User Group bibliography %%% archives, and the MathSciNet and zbMATH %%% databases. %%% %%% Numerous errors in the sources noted above %%% have been corrected. Spelling has been %%% verified with the UNIX spell and GNU ispell %%% programs using the exception dictionary %%% stored in the companion file with extension %%% .sok. %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by the biblabel software %%% developed for the BibNet Project. %%% %%% In this bibliography, entries are sorted in %%% publication order, with the help of %%% ``bibsort -bypages''. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

@Preamble{ "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" # "\ifx \undefined \boxtimes \let \boxtimes = \otimes \fi" # "\ifx \undefined \cprime \def \cprime {$'$}\fi" # "\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi" # "\ifx \undefined \mathbf \def \mathbf #1{{\bf #1}}\fi" # "\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" # "\ifx \undefined \mathfrak \let \mathfrak = \mathcal \fi" # "\ifx \undefined \mathscr \def \mathscr #1{{\cal #1}}\fi" # "\ifx \undefined \text \def \text #1{{\hbox{\rm #1}}}\fi" }

%%% ==================================================================== %%% Acknowledgement abbreviations:

@String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|"}

%%% ==================================================================== %%% Journal abbreviations:

@String{j-ELECTRON-COMMUN-PROBAB= "Electronic Communications in Probability"}

%%% ==================================================================== %%% Bibliography entries, sorted in publication order with %%% ``bibsort -byvolume'':

@Article{Kesten:1996:NCT, author = "Harry Kesten", title = "On the Non-Convexity of the Time Constant in First-Passage Percolation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "1", pages = "1:1--1:6", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v1-971", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60K35 (82B43)", MRnumber = "1386288 (98c:60142)", MRreviewer = "John C. Wierman", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/971", abstract = "We give a counterexample to a \url{http://www.ams.org/mathscinet-getitem?mr=33:6731} conjecture of Hammersley and Welsh (1965) about the convexity of the time constant in first-passage percolation, as a functional on the space of distribution functions. The present counterexample only works for first-passage percolation on $ Z^d $ for $d$ large.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "First-passage percolation, time constant, convexity.", } @Article{Kwapien:1996:PCB, author = "S. Kwapien and M. Pycia and W. Schachermayer", title = "A Proof of a Conjecture of {Bobkov} and {Houdr{\'e}}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "1", pages = "2:7--2:10", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v1-972", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60E05", MRnumber = "1386289 (97c:60032)", MRreviewer = "Christian Houdr{\'e}", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/972", abstract = "S. G. Bobkov and C. Houdr{\'e} recently posed the following question on the Internet (\url{http://www.sad.princeton.edu/sad/sad15/8}Problem posed in Stochastic Analysis Digest no. 15 (9/15/1995)): Let $ X, Y $ be symmetric i.i.d. random variables such that\par $$ P(|X + Y| / 2 \geq t) \leq P(|X| \geq t), $$ for each $ t > 0 $. Does it follow that $X$ has finite second moment (which then easily implies that $X$ is Gaussian)? In this note we give an affirmative answer to this problem and present a proof. Using a different method K. Oleszkiewicz has found another proof of this conjecture, as well as further related results.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Gaussian distribution.", } @Article{Dembo:1996:MDM, author = "Amir Dembo", title = "Moderate Deviations for Martingales with Bounded Jumps", journal = j-ELECTRON-COMMUN-PROBAB, volume = "1", pages = "3:11--3:17", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v1-973", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60F10 (60E15 60F17 60G42 60G44)", MRnumber = "1386290 (97k:60077)", MRreviewer = "Anatolii A. Pukhal{\cprime}ski{\u\i}", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/973", abstract = "We prove that the Moderate Deviation Principle (MDP) holds for the trajectory of a locally square integrable martingale with bounded jumps as soon as its quadratic covariation, properly scaled, converges in probability at an exponential rate. A consequence of this MDP is the tightness of the method of bounded martingale differences in the regime of moderate deviations.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Moderate deviations, martingales, bounded martingale differences.", } @Article{Werner:1996:BDE, author = "Wendelin Werner", title = "Bounds for Disconnection Exponents", journal = j-ELECTRON-COMMUN-PROBAB, volume = "1", pages = "4:19--4:28", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v1-974", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J65", MRnumber = "1386291 (97c:60206)", MRreviewer = "Jean Bertoin", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/974", abstract = "We slightly improve the upper bounds of disconnection exponents for planar Brownian motion that we derived in an earlier paper. We also give a proof of the lower bound $ 1 / (2 \pi) $ for the disconnection exponent for one path.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion, disconnection exponents", } @Article{Lawler:1996:DFP, author = "Gregory Lawler", title = "The dimension of the frontier of planar {Brownian} motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "1", pages = "5:29--5:47", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v1-975", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J65", MRnumber = "1386292 (97g:60110)", MRreviewer = "Paul McGill", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/975", abstract = "Let $B$ be a two dimensional Brownian motion and let the frontier of $ B[0, 1]$ be defined as the set of all points in $ B[0, 1]$ that are in the closure of the unbounded connected component of its complement. We prove that the Hausdorff dimension of the frontier equals $ 2 (1 - \alpha)$ where $ \alpha $ is an exponent for Brownian motion called the two-sided disconnection exponent. In particular, using an estimate on $ \alpha $ due to Werner, the Hausdorff dimension is greater than $ 1.015$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion, Hausdorff dimension, frontier, random fractals", } @Article{Puckette:1996:SCD, author = "Emily E. Puckette and Wendelin Werner", title = "Simulations and Conjectures for Disconnection Exponents", journal = j-ELECTRON-COMMUN-PROBAB, volume = "1", pages = "6:49--6:64", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v1-976", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J65 (65C05)", MRnumber = "1423905 (97k:60223)", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/976", abstract = "Using Monte-Carlo simulations, we estimate numerically disconnection exponents for planar Brownian motions. These simulations tend to confirm conjectures by Duplantier and Mandelbrot.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion, disconnection exponents", } @Article{Jansons:1996:END, author = "Kalvis M. Jansons", title = "Excursions Into a New Duality Relation for Diffusion Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "1", pages = "7:65--7:69", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v1-977", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60K35 (60J60)", MRnumber = "1423906 (97m:60149)", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/977", abstract = "This work was motivated by the recent work by H. Dette, J. Pitman and W. J. Studden on a new duality relation for random walks. In this note we consider the diffusion process limit of their result, and use the alternative approach of Ito excursion theory. This leads to a duality for Ito excursion rates.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Excursions, Diffusion Processes", } @Article{Benjamini:1996:PBM, author = "Itai Benjamini and Oded Schramm", title = "Percolation Beyond {$ \mathbf {Z}^d $}, Many Questions And a Few Answers", journal = j-ELECTRON-COMMUN-PROBAB, volume = "1", pages = "8:71--8:82", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v1-978", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60K35 (82B43)", MRnumber = "1423907 (97j:60179)", MRreviewer = "Olle H{\"a}ggstr{\"o}m", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/978", abstract = "A comprehensive study of percolation in a more general context than the usual $ Z^d $ setting is proposed, with particular focus on Cayley graphs, almost transitive graphs, and planar graphs. Results concerning uniqueness of infinite clusters and inequalities for the critical value $ p_c $ are given, and a simple planar example exhibiting uniqueness and non-uniqueness for different $ p > p_c $ is analyzed. Numerous varied conjectures and problems are proposed, with the hope of setting goals for future research in percolation theory.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Percolation, criticality, planar graph, transitive graph, isoperimetericinequality", } @Article{Dembo:1996:TAS, author = "Amir Dembo and Ofer Zeitouni", title = "Transportation Approach to Some Concentration Inequalities in Product Spaces", journal = j-ELECTRON-COMMUN-PROBAB, volume = "1", pages = "9:83--9:90", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v1-979", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60E15 (28A35)", MRnumber = "1423908 (98d:60035)", MRreviewer = "Iosif Pinelis", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/979", abstract = "Using a transportation approach we prove that for every probability measures $ P, Q_1, Q_2 $ on $ \Omega^N $ with $P$ a product measure there exist r.c.p.d. $ \nu_j$ such that $ \int \nu_j (\cdot |x) d P(x) = Q_j(\cdot)$ and\par $$ \int d P (x) \int \frac {dP}{dQ_1} (y)^\beta \frac {dP}{dQ_2} (z)^\beta (1 + \beta (1 - 2 \beta))^{f_N(x, y, z)} d \nu_1 (y|x) d \nu_2 (z|x) \le 1 \;, $$ for every $ \beta \in (0, 1 / 2)$. Here $ f_N$ counts the number of coordinates $k$ for which $ x_k \neq y_k$ and $ x_k \neq z_k$. In case $ Q_1 = Q_2$ one may take $ \nu_1 = \nu_2$. In the special case of $ Q_j(\cdot) = P(\cdot |A)$ we recover some of Talagrand's sharper concentration inequalities in product spaces.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Concentration inequalities, product spaces, transportation.", } @Article{Carmona:1996:SSO, author = "Rene Carmona and Stanislav Grishin and Lin Xu and Stanislav Molchanov", title = "Surface Stretching for {Ornstein--Uhlenbeck} Velocity Fields", journal = j-ELECTRON-COMMUN-PROBAB, volume = "2", pages = "1:1--1:11", year = "1996", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v2-980", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/980", abstract = "The present note deals with large time properties of the Lagrangian trajectories of a turbulent flow in $ R^2 $ and $ R^3 $. We assume that the flow is driven by an incompressible time-dependent random velocity field with Gaussian statistics. We also assume that the field is homogeneous in space and stationary and Markovian in time. Such velocity fields can be viewed as (possibly infinite dimensional) Ornstein--Uhlenbeck processes. In d spatial dimensions we established the (strict) positivity of the sum of the largest $ d - 1 $ Lyapunov exponents. As a consequences of this result, we prove the exponential stretching of surface areas (when $ d = 3$) and of curve lengths (when $ d = 2$.) This confirms conjectures found in the theory of turbulent flows.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Diffusion Processes, Lyapunov Exponent, Stochastic Flows.", } @Article{Carmona:1997:SSO, author = "Rene A. Carmona and Stanislav Grishin and Lin Xu and Stanislav Molchanov", title = "Surface stretching for {Ornstein} {Uhlenbeck} velocity fields", journal = j-ELECTRON-COMMUN-PROBAB, volume = "2", pages = "1:1--1:11", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v2-980", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60H25 (60H30)", MRnumber = "1448321 (99c:60132)", MRreviewer = "Nariyuki Minami", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Roberts:1997:GEH, author = "Gareth O. Roberts and Jeffrey S. Rosenthal", title = "Geometric ergodicity and hybrid {Markov} chains", journal = j-ELECTRON-COMMUN-PROBAB, volume = "2", pages = "2:13--2:25", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v2-981", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J35 (60F25 60J10)", MRnumber = "1448322 (99b:60122)", MRreviewer = "Esa Nummelin", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/981", abstract = "Various notions of geometric ergodicity for Markov chains on general state spaces exist. In this paper, we review certain relations and implications among them. We then apply these results to a collection of chains commonly used in Markov chain Monte Carlo simulation algorithms, the so-called hybrid chains. We prove that under certain conditions, a hybrid chain will {"inherit"} the geometric ergodicity of its constituent parts.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Markov chain Monte Carlo, hybrid Monte Carlo, geometric ergodicity, reversibility, spectral gap.", } @Article{Kiesel:1997:SLS, author = "R{\"u}diger Kiesel", title = "Strong laws and summability for sequences of {$ \phi $}-mixing random variables in {Banach} spaces", journal = j-ELECTRON-COMMUN-PROBAB, volume = "2", pages = "3:27--3:41", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v2-982", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60F15 (40A05 40J05 60B12)", MRnumber = "1448323 (2000a:60057)", MRreviewer = "A. Bozorgnia", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/982", abstract = "In this note the almost sure convergence of stationary, $ \varphi $-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the fulfillment of a certain integrability condition generalizing and extending the results for i.i.d. sequences. Furthermore we give via Baum-Katz type results an estimate for the rate of convergence in these laws.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Strong Laws, $varphi$-mixing, Summability.", } @Article{Barlow:1997:PBT, author = "Martin T. Barlow and Richard F. Bass and Krzysztof Burdzy", title = "Positivity of {Brownian} Transition Densities", journal = j-ELECTRON-COMMUN-PROBAB, volume = "2", pages = "4:43--4:51", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v2-983", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J35 (60J65)", MRnumber = "1484554 (99e:60166)", MRreviewer = "Lo{\"{\i}}c Chaumont", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/983", abstract = "Let $B$ be a Borel subset of $ R^d$ and let $ p(t, x, y)$ be the transition densities of Brownian motion killed on leaving $B$. Fix $x$ and $y$ in $B$. If $ p(t, x, y)$ is positive for one $t$, it is positive for every value of $t$. Some related results are given.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Transition densities, Brownian motion, eigenvalue expansion, fine topology, regular points.", } @Article{Jansons:1997:DTS, author = "Kalvis M. Jansons", title = "The Distribution of Time Spent by a Standard Excursion Above a Given Level, with Applications to Ring Polymers near a Discontinuity in Potential", journal = j-ELECTRON-COMMUN-PROBAB, volume = "2", pages = "5:53--5:58", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v2-984", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J65", MRnumber = "1484555 (98k:60141)", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/984", abstract = "The law for the time $ \tau_a $ spent by a standard Brownian excursion above a given level $ a > 0 $ is found using Ito excursion theory. This is achieved by conditioning the excursion to have exactly one mark of an independent Poisson process. Various excursion rates for excursions conditioned to have exactly $n$ marks are also given in terms of generating functions. This work has applications to the theory of ring polymers and end-attached polymers near a discontinuity in potential.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Standard Brownian Excursions, Brownian Bridges, Ring Polymers, End-Attached Polymers.", } @Article{Kaj:1997:SAS, author = "Ingemar Kaj and Serik Sagitov", title = "Superprocess Approximation For a Spatially Homogeneous Branching Walk", journal = j-ELECTRON-COMMUN-PROBAB, volume = "2", pages = "6:59--6:70", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v2-985", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J85 (60J80)", MRnumber = "1484556 (99a:60094)", MRreviewer = "Luis G. Gorostiza", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/985", abstract = "We present an alternative particle picture for super-stable motion. It is based on a non-local branching mechanism in discrete time and only trivial space motion.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Superprocess, critical branching walk, time-space-mass scaling, integral equations.", } @Article{Capitaine:1997:MRS, author = "Mireille Capitaine and Elton P. Hsu and Michel Ledoux", title = "Martingale Representation and a Simple Proof of Logarithmic {Sobolev} Inequalities on Path Spaces", journal = j-ELECTRON-COMMUN-PROBAB, volume = "2", pages = "7:71--7:81", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v2-986", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J65 (58D20 58G32 60B15 60D05 60H07)", MRnumber = "1484557 (99b:60136)", MRreviewer = "Shi Zan Fang", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/986", abstract = "We show how the Clark-Ocone-Haussmann formula for Brownian motion on a compact Riemannian manifold put forward by S. Fang in his proof of the spectral gap inequality for the Ornstein--Uhlenbeck operator on the path space can yield in a very simple way the logarithmic Sobolev inequality on the same space. By an appropriate integration by parts formula the proof also yields in the same way a logarithmic Sobolev inequality for the path space equipped with a general diffusion measure as long as the torsion of the corresponding Riemannian connection satisfies Driver's total antisymmetry condition.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Martingale representation, logarithmic Sobolev inequality, Brownian motion, Riemannian manifold", } @Article{Baryshnikov:1997:WSG, author = "Yuliy Baryshnikov", title = "{Wiener} Soccer and Its Generalization", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "1:1--1:11", year = "1997", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-987", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/987", abstract = "The trajectory of the ball in a soccer game is modelled by the Brownian motion on a cylinder, subject to elastic reflections at the boundary points (as proposed in [KPY]). The score is then the number of windings of the trajectory around the cylinder. We consider a generalization of this model to higher genus, prove asymptotic normality of the score and derive the covariance matrix. Further, we investigate the inverse problem: to what extent the underlying geometry can be reconstructed from the asymptotic score.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Wiener Process, Brownian Motion.", } @Article{Baryshnikov:1998:WSG, author = "Yuliy Baryshnikov", title = "{Wiener} soccer and its generalization", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "1--11", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-987", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J35 (60J65)", MRnumber = "1492035 (99c:60158)", MRreviewer = "Robert J. Adler", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Arcones:1998:LLN, author = "Miguel A. Arcones", title = "The Law of Large Numbers for {$U$}-statistics Under Absolute Regularity", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "2:13--2:19", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-988", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60F15", MRnumber = "1624866 (99d:60038)", MRreviewer = "Manfred Denker", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/988", abstract = "We prove the law of large numbers for $U$-statistics whose underlying sequence of random variables satisfies an absolute regularity condition ($ \beta $-mixing condition) under suboptimal conditions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Law of the large numbers, $U$-statistics, absolute regularity.", } @Article{Evans:1998:EIS, author = "Steven N. Evans and Yuval Peres", title = "Eventual Intersection for Sequences of {L{\'e}vy} Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "3:21--3:27", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-989", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J30 (60B15 60D05 60G17 60J45)", MRnumber = "1625695 (99g:60130)", MRreviewer = "Davar Khoshnevisan", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/989", abstract = "Consider the events $ \{ F_n \cap \bigcup_{k = 1}^{n - 1} F_k = \emptyset \} $, $ n \in N $, where $ (F_n)_{n = 1}^\infty $ is an i.i.d. sequence of stationary random subsets of a compact group $G$. A plausible conjecture is that these events will not occur infinitely often with positive probability if $ P \{ F_i \cap F_j \ne \emptyset \mid F_j \} > 0$ a.s. for $ i \ne j$. We present a counterexample to show that this condition is not sufficient, and give one that is. The sufficient condition always holds when $ F_n = \{ X_t^n : 0 \le t \le T \} $ is the range of a L{\'e}vy process $ X^n$ on the $d$-dimensional torus with uniformly distributed initial position and $ P \{ \exists 0 \le s, t \le T : X_s^i = X_t^j \} > 0$ for $ i \ne j$. We also establish an analogous result for the sequence of graphs $ \{ (t, X_t^n) : 0 \le t \le T \} $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "L{\'e}vy process, hitting probability, range, graph, random measure, random set, stationary", } @Article{Burdzy:1998:WCR, author = "Krzysztof Burdzy and Zhen-Qing Chen", title = "Weak Convergence of Reflecting {Brownian} Motions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "4:29--4:33", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-990", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J65", MRnumber = "1625707 (99d:60091)", MRreviewer = "Youngmee Kwon", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/990", abstract = "We show that if a sequence of domains $ D_k $ increases to a domain $D$ then the reflected Brownian motions in $ D_k$'s converge to the reflected Brownian motion in $D$, under mild technical assumptions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "reflected Brownian motion, weak convergence.", } @Article{Lawler:1998:LEW, author = "Gregory F. Lawler", title = "Loop-Erased Walks Intersect Infinitely Often in Four Dimensions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "5:35--5:42", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-991", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J15", MRnumber = "1637969 (99e:60156)", MRreviewer = "Thomas Polaski", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/991", abstract = "In this short note we show that the paths two independent loop-erased random walks in four dimensions intersect infinitely often. We actually prove the stronger result that the cut-points of the two walks intersect infinitely often.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random Walks, Loop-Erased Walks, Intersections", } @Article{Thalmaier:1998:SRH, author = "Anton Thalmaier", title = "Some Remarks on the Heat Flow for Functions and Forms", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "6:43--6:49", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-992", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "58G32 (58G11 60G44)", MRnumber = "1637977 (99i:58157)", MRreviewer = "Elton Pei Hsu", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/992", abstract = "This note is concerned with the differentiation of heat semigroups on Riemannian manifolds. In particular, the relation $ d P_t f = P_t d f $ is investigated for the semigroup generated by the Laplacian with Dirichlet boundary conditions. By means of elementary martingale arguments it is shown that well-known properties which hold on complete Riemannian manifolds fail if the manifold is only BM-complete. In general, even if $M$ is flat and $f$ smooth of compact support, $ \Vert d P_t f \Vert_\infty $ cannot be estimated on compact time intervals in terms of $f$ or $ d f$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Heat semigroup, heat equation, Brownian motion, damped parallel translation, Ricci curvature.", } @Article{Fargason:1998:PDB, author = "Chad Fargason", title = "Percolation dimension of {Brownian} motion in {$ \mathbf {R}^3 $}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "7:51--7:63", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-993", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J65", MRnumber = "1641070 (99g:60149)", MRreviewer = "Davar Khoshnevisan", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/993", abstract = "Let $ B(t) $ be a Brownian motion in $ R^3 $. A {\em subpath\/} of the Brownian path $ B[0, 1] $ is a continuous curve $ \gamma (t) $, where $ \gamma [0, 1] \subseteq B[0, 1] $ , $ \gamma (0) = B(0) $, and $ \gamma (1) = B(1) $. It is well-known that any subset $S$ of a Brownian path must have Hausdorff dimension $ \text {dim} (S) \leq 2.$ This paper proves that with probability one there exist subpaths of $ B[0, 1]$ with Hausdorff dimension strictly less than 2. Thus the percolation dimension of Brownian motion in $ R^3$ is strictly less than 2.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Percolation dimension, boundary dimension, intersection exponent", } @Article{Rincon:1998:EDD, author = "L. A. Rincon", title = "Estimates for the Derivative of Diffusion Semigroups", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "8:65--8:74", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-994", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J60 (47D07 60H10)", MRnumber = "1641074 (99g:60144)", MRreviewer = "Ren Ming Song", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/994", abstract = "Let $ \{ P_t \}_{t \ge 0} $ be the transition semigroup of a diffusion process. It is known that $ P_t $ sends continuous functions into differentiable functions so we can write $ D P_t f $. But what happens with this derivative when $ t \to 0 $ and $ P_0 f = f $ is only continuous?. We give estimates for the supremum norm of the Frechet derivative of the semigroups associated with the operators $ {\cal A} + V $ and $ {\cal A} + Z \cdot \nabla $ where $ {\cal A} $ is the generator of a diffusion process, $V$ is a potential and $Z$ is a vector field.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Diffusion Semigroups, Diffusion Processes, Stochastic Differential Equations.", xxtitle = "Estimates for the derivatives of diffusion semigroups", } @Article{Ryznar:1998:UUB, author = "Micha{\l} Ryznar and Tomasz {\.Z}ak", title = "Uniform Upper Bound for a Stable Measure of a Small Ball", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "9:75--9:78", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-995", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60E07 (46B20 46G12)", MRnumber = "1645592 (99g:60034)", MRreviewer = "Aleksandr Koldobsky", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/995", abstract = "P. Hitczenko, S. Kwapien, W. N. Li, G. Schechtman, T. Schlumprecht and J. Zinn stated the following conjecture. Let $ \mu $ be a symmetric $ \alpha $-stable measure on a separable Banach space and $B$ a centered ball such that $ \mu (B) \le b$. Then there exists a constant $ R(b)$, depending only on $b$, such that $ \mu (t B) \le R(b)t \mu (B)$ for all $ 0 < t < 1$. We prove that the above inequality holds but the constant $R$ must depend also on $ \alpha $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "stable measure, small ball", } @Article{Aldous:1998:BEC, author = "David J. Aldous", title = "{Brownian} Excursion Conditioned on Its Local Time", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "10:79--10:90", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-996", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J55 (60J65)", MRnumber = "1650567 (99m:60115)", MRreviewer = "Ingemar Kaj", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/996", abstract = "For a function $ \ell $ satisfying suitable integrability (but not continuity) requirements, we construct a process $ (B^\ell_u, 0 \leq u \leq 1) $ interpretable as Brownian excursion conditioned to have local time $ \ell (\cdot) $ at time $1$. The construction is achieved by first defining a non-homogeneous version of Kingman's coalescent and then applying the general theory in Aldous (1993) relating excursion-type processes to continuum random trees. This complements work of Warren and Yor (1997) on the Brownian burglar.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian excursion, continuum random tree, Kingman's coalescent, local time.", } @Article{Marchal:1998:BBT, author = "Philippe Marchal", title = "The Best Bounds in a Theorem of {Russell Lyons}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "11:91--11:94", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-997", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60K35 (05C05)", MRnumber = "1650563 (99j:60156)", MRreviewer = "Wolfgang Woess", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/997", abstract = "We sharpen a bound in a theorem of Russell Lyons for percolation on a tree and associated random walk.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random Walks, Percolation, Tree.", } @Article{Carmona:1998:FBM, author = "Philippe Carmona and Laure Coutin", title = "Fractional {Brownian} Motion and the {Markov} Property", journal = j-ELECTRON-COMMUN-PROBAB, volume = "3", pages = "12:95--12:107", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v3-998", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60H35 (65C50)", MRnumber = "1658690 (2000b:60163)", MRreviewer = "Corinne Berzin", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/998", abstract = "Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This leads naturally to:\par \begin{itemize} \item An efficient algorithm to approximate the process. \item An ergodic theorem which applies to functionals of the type\par $$ \int_0^t \phi (V_h(s)), d s \quad {\rm where~} \quad V_h(s) = \int_0^s h(s - u), d B_u. $$ \end{itemize} where $B$ is a real Brownian motion.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Gaussian processes, Markov Processes, Numerical Approximation, Ergodic Theorem.", } @Article{Handa:1998:LBT, author = "Kenji Handa", title = "A Lower Bound for Time Correlation of Lattice Gases", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "1:1--1:8", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-999", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/999", abstract = "The lattice gas model in equilibrium is considered. We give a lower bound of the density-density time correlation for large time, which involves the bulk diffusion matrix in a physically natural way.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Lattice gas models, correlation function, the bulk diffusion matrix.", } @Article{Handa:1999:LBT, author = "Kenji Handa", title = "A lower bound for time correlation of lattice gases", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "1--8", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-999", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "82C20 (60K35 82C22)", MRnumber = "1691652 (2000g:82020)", MRreviewer = "Raphael Lefevere", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Hooghiemstra:1999:OTB, author = "Gerard Hooghiemstra", title = "On the Occupation Time of {Brownian} Excursion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "8:61--8:64", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1006", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J65", MRnumber = "1711595 (2001h:60144)", MRreviewer = "Robert J. Adler", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1006", abstract = "Recently, Kalvin M. Jansons derived in an elegant way the Laplace transform of the time spent by an excursion above a given level $ a > 0 $. This result can also be derived from previous work of the author on the occupation time of the excursion in the interval $ (a, a + b] $, by sending $ b \to \infty $. Several alternative derivations are included.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian excursion, occupation time.", } @Article{Evans:1999:IES, author = "Steven N. Evans and Xiaowen Zhou", title = "Identifiability of Exchangeable Sequences with Identically Distributed Partial Sums", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "2:9--2:13", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1000", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60G09", MRnumber = "1691653 (2000e:60055)", MRreviewer = "N. C. Weber", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1000", abstract = "Consider two exchangeable sequences $ (X_k)_{k \in N} $ and $ (\hat {X}_k)_{k \in N} $ with the property that $ S_n \equiv \sum_{k = 1}^n X_k $ and $ \hat {S}_n \equiv \sum_{k = 1}^n \hat {X}_k $ have the same distribution for all $ n \in N $. David Aldous posed the following question. Does this imply that the two exchangeable sequences have the same joint distributions? We give an example that shows the answer to Aldous' question is, in general, in the negative. On the other hand, we show that the joint distributions of an exchangeable sequence can be recovered from the distributions of its partial sums if the sequence is a countable mixture of i.i.d. sequences that are either nonnegative or have finite moment generating functions in some common neighbourhood of zero.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "exchangeability, de Finetti's theorem, characteristics function, Laplace transform, moment generating function", } @Article{Matsumoto:1999:SCP, author = "Hiroyuki Matsumoto and Marc Yor", title = "Some Changes of Probabilities Related to a Geometric {Brownian} Motion Version of {Pitman}'s {$ 2 M - X $} Theorem", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "3:15--3:23", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1001", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J60 (60J65)", MRnumber = "1703607 (2000e:60130)", MRreviewer = "F. B. Knight", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1001", abstract = "Rogers-Pitman have shown that the sum of the absolute value of $ B^{(\mu)} $, Brownian motion with constant drift $ \mu $, and its local time $ L^{(\mu)} $ is a diffusion $ R^{(\mu)} $. We exploit the intertwining relation between $ B^{(\mu)} $ and $ R^{(\mu)} $ to show that the same addition operation performed on a one-parameter family of diffusions $ {X^{(\alpha, \mu)}}_{\alpha \in {\mathbf R}_+} $ yields the same diffusion $ R^{(\mu)} $. Recently we obtained an exponential analogue of the Rogers-Pitman result. Here we exploit again the corresponding intertwining relationship to yield a one-parameter family extension of our result.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Diffusion Process, Geometric Brownian Motion, Markov Intertwining Kernel, (strict) Local Martingale, Explosion.", } @Article{Warren:1999:RDA, author = "Jon Warren", title = "On a Result of {David Aldous} Concerning the Trees in a Conditioned Excursion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "4:25--4:29", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1002", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J55", MRnumber = "1703608 (2000f:60121)", MRreviewer = "David J. Aldous", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1002", abstract = "The law of a random tree constructed within a Brownian excursion is calculated conditional on knowing the occupation measure of the excursion. In previous work David Aldous has used random walk approximations to obtain this result. Here it is deduced from Le Gall's description of the tree in the unconditioned excursion.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian excursion, random tree, local time.", } @Article{Bertoin:1999:CBP, author = "Jean Bertoin and Jim Pitman and Juan {Ruiz de Chavez}", title = "Constructions of a {Brownian} Path With a Given Minimum", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "5:31--5:37", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1003", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J65 (60G17)", MRnumber = "1703609 (2000j:60097)", MRreviewer = "Paul McGill", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1003", abstract = "We construct a Brownian path conditioned on its minimum value over a fixed time interval by a simple transformation of a Brownian bridge.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Conditioned Brownian motion, path transformations", } @Article{Schramm:1999:TCH, author = "Oded Schramm and Boris Tsirelson", title = "Trees, Not Cubes: Hypercontractivity, Cosiness, and Noise Stability", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "6:39--6:49", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1004", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J10 (05C05 42C10 46E39)", MRnumber = "1711603 (2000k:60143)", MRreviewer = "Laurent Miclo", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1004", abstract = "Noise sensitivity of functions on the leaves of a binary tree is studied, and a hypercontractive inequality is obtained. We deduce that the spider walk is not noise stable.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "hypercontractivity, cosiness, noise stability, noise sensitivity", } @Article{Lindvall:1999:STS, author = "Torgny Lindvall", title = "On {Strassen}'s Theorem on Stochastic Domination", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "7:51--7:59", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1005", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60B05 (60E15 60J05)", MRnumber = "1711599 (2000k:60006)", MRreviewer = "George L. O'Brien", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1005", abstract = "The purpose of this note is to make available a reasonably complete and straightforward proof of Strassen's theorem on stochastic domination, and to draw attention to the original paper. We also point out that the maximal possible value of $ P(Z = Z') $ is actually not reduced by the requirement $ Z \leq Z' $. Here, $ Z, Z' $ are stochastic elements that Strassen's theorem states exist under a stochastic domination condition. The consequence of that observation to stochastically monotone Markov chains is pointed out. Usually the theorem is formulated with the assumption that $ \leq $ is a partial ordering; the proof reveals that a pre-ordering suffices.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Strassen's theorem, coupling, pre-ordering, maximal diagonal probability", } @Article{Li:1999:RPF, author = "Zenghu Li and Tokuzo Shiga and Lihua Yao", title = "A Reversibility Problem for {Fleming--Viot} Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "9:65--9:76", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1007", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60G57 (60J60)", MRnumber = "1711591 (2001e:60097)", MRreviewer = "Sylvie Roelly", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1007", abstract = "Fleming--Viot processes incorporating mutation and selection are considered. It is well-known that if the mutation factor is of uniform type, the process has a reversible stationary distribution, and it has been an open problem to characterize the class of the processes that have reversible stationary distributions. This paper proves that if a Fleming--Viot process has a reversible stationary distribution, then the associated mutation operator is of uniform type.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Fleming--Viot processes, measure-valued diffusion, reversibility, Dirichlet space", } @Article{Lewis:1999:CM, author = "Thomas M. Lewis and Geoffrey Pritchard", title = "Correlation Measures", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "10:77--10:85", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1008", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60E15", MRnumber = "1716783 (2000j:60023)", MRreviewer = "Christian Houdr{\'e}", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1008", abstract = "We study a class of Borel probability measures, called correlation measures. Our results are of two types: first, we give explicit constructions of non-trivial correlation measures; second, we examine some of the properties of the set of correlation measures. In particular, we show that this set of measures has a convexity property. Our work is related to the so-called Gaussian correlation conjecture.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "correlation measures, Gaussian correlation inequality", } @Article{Guillotin:1999:EOM, author = "Nadine Guillotin", title = "Edge Occupation Measure for a Reversible {Markov} Chain", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "11:87--11:90", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1009", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60J10 (60F05 60F10)", MRnumber = "1741735 (2001g:60169)", MRreviewer = "Wolfgang K{\"o}nig", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1009", abstract = "In this note, we study the Gaussian fluctuations of the edge occupation measure for a reversible Markov chain and give a nice description of the covariance matrix. Then we give some large deviations results concerning this occupation measure.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Markov Chain, Limit theorems, Large deviations principle", } @Article{Cranston:1999:LEI, author = "Michael Cranston and Michael Scheutzow and David Steinsaltz", title = "Linear Expansion of Isotropic {Brownian} Flows", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "12:91--12:101", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1010", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60H15 (60J65)", MRnumber = "1741738 (2001d:60068)", MRreviewer = "R{\'e}mi L{\'e}andre", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1010", abstract = "We consider an isotropic Brownian flow on $ R^d $ for $ d \geq 2 $ with a positive Lyapunov exponent, and show that any nontrivial connected set almost surely contains points whose distance from the origin under the flow grows linearly with time. The speed is bounded below by a fixed constant, which may be computed from the covariance tensor of the flow. This complements earlier work, which showed that stochastic flows with bounded local characteristics and zero drift cannot grow at a linear rate faster than linear.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stochastic flows, Brownian flows, stochastic differential equations, martingale fields, Lyapunov exponents", } @Article{Csaki:1999:CEB, author = "Endre Cs{\'a}ki and Davar Khoshnevisan and Zhan Shi", title = "Capacity Estimates, Boundary Crossings and the {Ornstein--Uhlenbeck} Process in {Wiener} Space", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "13:103--13:109", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1011", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60G15 (60G40 60G60 60J45 60J65)", MRnumber = "1741736 (2001g:60083)", MRreviewer = "Shi Zan Fang", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1011", abstract = "Let $ T_1 $ denote the first passage time to 1 of a standard Brownian motion. It is well known that as $ \lambda $ goes to infinity, $ P \{ T_1 > \lambda \} $ goes to zero at rate $ c \lambda^{-1 / 2} $, where $c$ equals $ (2 / \pi)^{1 / 2}$. The goal of this note is to establish a quantitative, infinite dimensional version of this result. Namely, we will prove the existence of positive and finite constants $ K_1$ and $ K_2$, such that for all $ \lambda > e^e$, \par $$ K_1 \lambda^{-1 / 2} \leq \text {Cap} \{ T_1 > \lambda \} \leq K_2 \lambda^{-1 / 2} \log^3 (\lambda) \cdot \log \log (\lambda), $$ where `$ \log $' denotes the natural logarithm, and $ \text {Cap}$ is the Fukushima-Malliavin capacity on the space of continuous functions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Capacity on Wiener space, quasi-sure analysis, Ornstein--Uhlenbeck process, Brownian sheet.", } @Article{Li:1999:GCI, author = "Wenbo V. Li", title = "A {Gaussian} Correlation Inequality and its Applications to Small Ball Probabilities", journal = j-ELECTRON-COMMUN-PROBAB, volume = "4", pages = "14:111--14:118", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v4-1012", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60G15 (60E15)", MRnumber = "1741737 (2001j:60074)", MRreviewer = "Qi Man Shao", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1012", abstract = "We present a Gaussian correlation inequality which is closely related to a result of Schechtman, Schlumprecht and Zinn (1998) on the well-known Gaussian correlation conjecture. The usefulness of the inequality is demonstrated by several important applications to the estimates of small ball probability.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Small ball probabilities, Gaussian correlation inequality", } @Article{Schweinsberg:1999:NSC, author = "Jason Schweinsberg", title = "A Necessary and Sufficient Condition for the Lambda-Coalescent to Come Down from Infinity", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "1:1--1:11", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1013", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1013", abstract = "Let $ \Pi_{\infty } $ be the standard $ \Lambda $-coalescent of Pitman, which is defined so that $ \Pi_{\infty }(0)$ is the partition of the positive integers into singletons, and, if $ \Pi_n$ denotes the restriction of $ \Pi_{\infty }$ to $ \{ 1, \ldots, n \} $, then whenever $ \Pi_n(t)$ has $b$ blocks, each $k$-tuple of blocks is merging to form a single block at the rate $ \lambda_{b, k}$, where $ \lambda_{b, k} = \int_0^1 x^{k - 2} (1 - x)^{b - k} \Lambda (d x)$ for some finite measure $ \Lambda $. We give a necessary and sufficient condition for the $ \Lambda $-coalescent to ``come down from infinity'', which means that the partition $ \Pi_{\infty }(t)$ almost surely consists of only finitely many blocks for all $ t > 0$. We then show how this result applies to some particular families of $ \Lambda $-coalescents.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "coalescent, Kochen-Stone Lemma", } @Article{Limic:1999:BLP, author = "Vlada Limic", title = "On the Behavior of {LIFO} Preemptive Resume Queues in Heavy Traffic", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "2:13--2:27", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1014", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1014", abstract = "This paper studies heavy traffic behavior of a G/G/1 last-in-first-out (LIFO) preemptive resume queue, by extending the techniques developed in Limic (1999). The queue length process exhibits a perhaps unexpected heavy traffic behavior. The diffusion limit depends on the type of arrivals (and services) in a fairly intricate way, related to the Wiener-Hopf factorization for random walks.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "LIFO queue, heavy traffic, measure-valued process, branching, feedback, renewal, Wiener-Hopf factorization", } @Article{Marchal:1999:LER, author = "Philippe Marchal", title = "Loop-Erased Random Walks, Spanning Trees and {Hamiltonian} Cycles", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "4:39--4:50", year = "1999", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1016", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1016", abstract = "We establish a formula for the distribution of loop-erased random walks at certain random times. Several classical results on spanning trees, including Wilson's algorithm, follow easily, as well as a method to construct random Hamiltonian cycles.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Loop-erased random walk, spanning tree, Wilson's algorithm", } @Article{Telcs:2000:TPE, author = "Andras Telcs", title = "Transition Probability Estimates for Reversible {Markov} Chains", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "3:29--3:37", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1015", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1015", abstract = "This paper provides transition probability estimates of transient reversible Markov chains. The key condition of the result is the spatial symmetry and polynomial decay of the Green's function of the chain.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random walks, reversible Markov chains, fractals, dimensions", } @Article{Bertoin:2000:CMC, author = "Jean Bertoin", title = "The Convex Minorant of the {Cauchy} Process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "5:51--5:55", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1017", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1017", abstract = "We determine the law of the convex minorant $ (M_s, s \in [0, 1]) $ of a real-valued Cauchy process on the unit time interval, in terms of the gamma process. In particular, this enables us to deduce that the paths of $M$ have a continuous derivative, and that the support of the Stieltjes measure $ d M'$ has logarithmic dimension one.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Cauchy process, Gamma process, convex minorant", } @Article{Barlow:2000:VSB, author = "Martin Barlow and Krzysztof Burdzy and Haya Kaspi and Avi Mandelbaum", title = "Variably Skewed {Brownian} Motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "6:57--6:66", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1018", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1018", abstract = "Given a standard Brownian motion $B$, we show that the equation\par $$ X_t = x_0 + B_t + \beta (L_t^X), t \geq 0, $$ has a unique strong solution $X$. Here $ L^X$ is the symmetric local time of $X$ at $0$, and $ \beta $ is a given differentiable function with $ \beta (0) = 0$, whose derivative is always in $ ( - 1, 1)$. For a linear function $ \beta $, the solution is the familiar skew Brownian motion.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Skew Brownian motion, Brownian motion, stochastic differential equation, local time", } @Article{Angel:2000:LWS, author = "Omer Angel and Itai Benjamini and Yuval Peres", title = "A Large {Wiener} Sausage from Crumbs", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "7:67--7:71", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1019", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1019", abstract = "Let $ B(t) $ denote Brownian motion in $ R^d $. It is a classical fact that for any Borel set $A$ in $ R^d$, the volume $ V_1 (A)$ of the Wiener sausage $ B[0, 1] + A$ has nonzero expectation iff $A$ is nonpolar. We show that for any nonpolar $A$, the random variable $ V_1 (A)$ is unbounded.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion, capacity, polar set, Wiener sausage.", } @Article{Sepanski:2000:WLL, author = "Steven Sepanski and Zhidong Pan", title = "A Weak Law of Large Numbers for the Sample Covariance Matrix", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "8:73--8:76", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1020", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1020", abstract = "In this article we consider the sample covariance matrix formed from a sequence of independent and identically distributed random vectors from the generalized domain of attraction of the multivariate normal law. We show that this sample covariance matrix, appropriately normalized by a nonrandom sequence of linear operators, converges in probability to the identity matrix.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Law of large numbers, affine normalization, sample covariance, central limit theorem, domain of attraction, generalized domain of attraction, multivariate t statistic", } @Article{Fill:2000:CSF, author = "James Fill and Svante Janson", title = "A Characterization of the Set of Fixed Points of the {Quicksort} Transformation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "9:77--9:84", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1021", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1021", abstract = "The limiting distribution $ \mu $ of the normalized number of key comparisons required by the Quicksort sorting algorithm is known to be the unique fixed point of a certain distributional transformation $T$ - unique, that is, subject to the constraints of zero mean and finite variance. We show that a distribution is a fixed point of $T$ if and only if it is the convolution of $ \mu $ with a Cauchy distribution of arbitrary center and scale. In particular, therefore, $ \mu $ is the unique fixed point of $T$ having zero mean.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Quicksort, fixed point, characteristic function, smoothing transformation, domain of attraction, coupling, integral equation", } @Article{Jonasson:2000:CTP, author = "Johan Jonasson and Oded Schramm", title = "On the Cover Time of Planar Graphs", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "10:85--10:90", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1022", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1022", abstract = "The cover time of a finite connected graph is the expected number of steps needed for a simple random walk on the graph to visit all the vertices. It is known that the cover time on any $n$-vertex, connected graph is at least $ \bigl (1 + o(1) \bigr)n \log n$ and at most $ \bigl (1 + o(1) \bigr) \frac {4}{27}n^3$. This paper proves that for bounded-degree planar graphs the cover time is at least $ c n(\log n)^2$, and at most $ 6 n^2$, where $c$ is a positive constant depending only on the maximal degree of the graph. The lower bound is established via use of circle packings.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "effective resistance, commute time, hitting time, difference time, circle packing, triangulation", } @Article{Fitzsimmons:2000:SFM, author = "P. Fitzsimmons", title = "Strict Fine Maxima", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "11:91--11:94", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1023", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1023", abstract = "We provide a simple probabilistic proof of a result of J. Kr{\'a}l and I. Netuka: If $f$ is a measurable real-valued function on $ \mathbb {R}^d$ ($ d > 1$) then the set of points at which $f$ has a strict {\em fine\/} local maximum value is polar.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion, fine topology, local maxima, optional projection.", } @Article{Devroye:2000:PSQ, author = "Luc Devroye and James Fill and Ralph Neininger", title = "Perfect Simulation from the {Quicksort} Limit Distribution", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "12:95--12:99", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1024", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib; http://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ecp.ejpecp.org/article/view/1024", abstract = "The weak limit of the normalized number of comparisons needed by the Quicksort algorithm to sort $n$ randomly permuted items is known to be determined implicitly by a distributional fixed-point equation. We give an algorithm for perfect random variate generation from this distribution.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Quicksort, random variate generation, simulation, perfect simulation, rejection method, Monte Carlo method, fixed-point equation", } @Article{Briand:2000:CCT, author = "Philippe Briand and Fran{\c{c}}ois Coquet and Ying Hu and Jean M{\'e}min and Shige Peng", title = "A Converse Comparison Theorem for {BSDEs} and Related Properties of $g$-Expectation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "13:101--13:117", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1025", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1025", abstract = "In [1], Z. Chen proved that, if for each terminal condition $ \xi $, the solution of the BSDE associated to the standard parameter $ (\xi, g_1) $ is equal at time $ t = 0 $ to the solution of the BSDE associated to $ (\xi, g_2) $ then we must have $ g_1 \equiv g_2 $. This result yields a natural question: what happens in the case of an inequality in place of an equality? In this paper, we try to investigate this question and we prove some properties of ``$g$-expectation'', notion introduced by S. Peng in [8].", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Backward stochastic differential equations, comparison theorem.", } @Article{Guionnet:2000:CSM, author = "Alice Guionnet and Ofer Zeitouni", title = "Concentration of the Spectral Measure for Large Matrices", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "14:119--14:136", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1026", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1026", abstract = "We derive concentration inequalities for functions of the empirical measure of eigenvalues for large, random, self adjoint matrices, with not necessarily Gaussian entries. The results presented apply in particular to non-Gaussian Wigner and Wishart matrices. We also provide concentration bounds for non commutative functionals of random matrices.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random Matrices, Concentration inequalities, non-commutative functionals.", } @Article{Kuznetsov:2000:USG, author = "Sergei Kuznetsov", title = "On Uniqueness of a Solution of {$ L u = u^\alpha $} with Given Trace", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "15:137--15:147", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1027", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1027", abstract = "A boundary trace $ (\Gamma, \nu) $ of a solution of $ \Delta u = u^\alpha $ in a bounded smooth domain in $ \mathbb {R}^d $ was first constructed by Le Gall \cite{LGOne} who described all possible traces for $ \alpha = 2, d = 2 $ in which case a solution is defined uniquely by its trace. In a number of publications, Marcus, V{\'e}ron, Dynkin and Kuznetsov gave analytic and probabilistic generalization of the concept of trace to the case of arbitrary $ \alpha > 1, d \ge 1 $. However, it was shown by Le Gall that the trace, in general, does not define a solution uniquely in case $ d \ge (\alpha + 1) / (\alpha - 1) $. He offered a sufficient condition for the uniqueness and conjectured that a uniqueness should be valid if the singular part $ \Gamma $ of the trace coincides with the set of all explosion points of the measure $ \nu $. Here, we establish a necessary condition for the uniqueness which implies a negative answer to the above conjecture.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "superdiffusion, moderate solutions, sigma-moderate solutions, stochastic boundary values, trace of a solution, explosion points.", } @Article{Simon:2000:SME, author = "Thomas Simon", title = "Support of a {Marcus} equation in Dimension $1$", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "16:149--16:157", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1028", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1028", abstract = "The purpose of this note is to give a support theorem in the Skorohod space for a one-dimensional Marcus differential equation driven by a L{\'e}vy process, without any assumption on the latter. We also give a criterion ensuring that the support of the equation is the whole Skorohod space. This improves, in dimension 1, a result of H. Kunita.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Fagnola:2000:MSQ, author = "Franco Fagnola and Stephen Wills", title = "Mild Solutions of Quantum Stochastic Differential Equations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "5", pages = "17:158--17:171", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v5-1029", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1029", abstract = "We introduce the concept of a mild solution for the right Hudson-Parthasarathy quantum stochastic differential equation, prove existence and uniqueness results, and show the correspondence between our definition and similar ideas in the theory of classical stochastic differential equations. The conditions that a process must satisfy in order for it to be a mild solution are shown to be strictly weaker than those for it to be a strong solution by exhibiting a class of coefficient matrices for which a mild unitary solution can be found, but for which no strong solution exists.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Quantum stochastic, stochastic differential equation, mild solution", } @Article{Briand:2001:DTT, author = "Philippe Briand and Bernard Delyon and Jean M{\'e}min", title = "{Donsker}-Type Theorem for {BSDEs}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "1:1--1:14", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1030", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1030", abstract = "This paper is devoted to the proof of Donsker's theorem for backward stochastic differential equations (BSDEs for short). The main objective is to give a simple method to discretize in time a BSDE. Our approach is based upon the notion of ``convergence of filtrations'' and covers the case of a $ (y, z)$-dependent generator.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Backward stochastic differential equation (BSDE), stability of BSDEs, weak convergence of filtrations, discretization.", } @Article{Marcus:2001:NID, author = "Michael Marcus and Jan Rosinski", title = "{$ L^1 $}-Norm of Infinitely Divisible Random Vectors and Certain Stochastic Integrals", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "2:15--2:29", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1031", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1031", abstract = "Equivalent upper and lower bounds for the $ L^1 $ norm of Hilbert space valued infinitely divisible random variables are obtained and used to find bounds for different types of stochastic integrals.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Infinitely divisible random variables, stochastic integrals", } @Article{Atar:2001:BDP, author = "Rami Atar and Siva Athreya and Min Kang", title = "Ballistic Deposition on a Planar Strip", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "3:31--3:38", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1032", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1032", abstract = "We consider ballistic diffusion limited aggregation on a finite strip $ [0, L - 1] $ times $ \mathbb {Z}_+ $ in $ \mathbb {Z}^2 $ for some $L$ in $ \mathbb {Z}_+$. We provide numerical bounds on the growth in the height process.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Ballistic, Deposition, Diffusion Limited Aggregation.", } @Article{Giacomin:2001:RTS, author = "Giambattista Giacomin and Gustavo Posta", title = "On Recurrent and Transient Sets of Inhomogeneous Symmetric Random Walks", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "4:39--4:53", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1033", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1033", abstract = "We consider a continuous time random walk on the $d$-dimensional lattice $ \mathbb {Z}^d$: the jump rates are time dependent, but symmetric and strongly elliptic with ellipticity constants independent of time. We investigate the implications of heat kernel estimates on recurrence-transience properties of the walk and we give conditions for recurrence as well as for transience: we give applications of these conditions and discuss them in relation with the (optimal) Wiener test available in the time independent context. Our approach relies on estimates on the time spent by the walk in a set and on a 0-1 law. We show also that, still via heat kernel estimates, one can avoid using a 0-1 law, achieving this way quantitative estimates on more general hitting probabilities.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Inhomogeneous Symmetric Random Walks, Heat Kernel Estimates, Recurrence-Transience, Hitting Probabilities, Wiener test, Paley-Zygmund inequality", } @Article{Panchenko:2001:NTC, author = "Dmitriy Panchenko", title = "A Note on {Talagrand}'s Concentration Inequality", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "5:55--5:65", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1034", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1034", abstract = "In this paper we revisit Talagrand's proof of concentration inequality for empirical processes. We give a different proof of the main technical lemma that guarantees the existence of a certain kernel. Moreover, we generalize the result of Talagrand to a family of kernels which in one particular case allows us to produce the Poissonian bound without using the truncation argument. We also give some examples of applications of the abstract concentration inequality to empirical processes that demonstrate some interesting properties of Talagrand's kernel method.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Concentration of measure, empirical processes", } @Article{Swart:2001:DSW, author = "Jan Swart", title = "A {$2$}-Dimensional {SDE} Whose Solutions are Not Unique", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "6:67--6:71", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1035", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1035", abstract = "In 1971, Yamada and Watanabe showed that pathwise uniqueness holds for the SDE $ d X = \sigma (X)d B $ when sigma takes values in the n-by-m matrices and satisfies $ | \sigma (x) - \sigma (y)| < |x - y| \log (1 / |x - y|)^{1 / 2} $. When $ n = m = 2 $ and $ \sigma $ is of the form $ \sigma_{ij}(x) = \delta_{ij}s(x) $, they showed that this condition can be relaxed to $ | \sigma (x) - \sigma (y)| < |x - y| \log (1 / |x - y|) $, leaving open the question whether this is true for general $ 2 \times m $ matrices. We construct a $ 2 \times 1 $ matrix-valued function which negatively answers this question. The construction demonstrates an unexpected effect, namely, that fluctuations in the radial direction may stabilize a particle in the origin.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stochastic differential equation, pathwise uniqueness / strong uniqueness, diffusion process.", } @Article{Hambly:2001:PTS, author = "B. Hambly and James Martin and Neil O'Connell", title = "{Pitman}'s {$ 2 M - X $} Theorem for Skip-Free Random Walks with {Markovian} Increments", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "7:73--7:77", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1036", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1036", abstract = "Let $ (\xi_k, k \ge 0) $ be a Markov chain on $ {-1, + 1} $ with $ \xi_0 = 1 $ and transition probabilities $ P(\xi_{k + 1} = 1 | \xi_k = 1) = a > b = P(\xi_{k + 1} = - 1 | \xi_k = - 1) $. Set $ X_0 = 0 $, $ X_n = \xi_1 + \cdots + \xi_n $ and $ M_n = \max_{0 \le k \le n}X_k $. We prove that the process $ 2 M - X $ has the same law as that of $X$ conditioned to stay non-negative.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Pitman's representation, three-dimensional Bessel process, telegrapher's equation, queue, Burke's theorem, quasireversibility.", } @Article{Bandyopadhyay:2001:HCF, author = "Antar Bandyopadhyay and David Aldous", title = "How to Combine Fast Heuristic {Markov} Chain {Monte Carlo} with Slow Exact Sampling", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "8:79--8:89", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1037", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1037", abstract = "Given a probability law $ \pi $ on a set $S$ and a function $ g : S \rightarrow R$, suppose one wants to estimate the mean $ \bar {g} = \int g d \pi $. The Markov Chain Monte Carlo method consists of inventing and simulating a Markov chain with stationary distribution $ \pi $. Typically one has no a priori bounds on the chain's mixing time, so even if simulations suggest rapid mixing one cannot infer rigorous confidence intervals for $ \bar {g}$. But suppose there is also a separate method which (slowly) gives samples exactly from $ \pi $. Using $n$ exact samples, one could immediately get a confidence interval of length $ O(n^{-1 / 2})$. But one can do better. Use each exact sample as the initial state of a Markov chain, and run each of these $n$ chains for $m$ steps. We show how to construct confidence intervals which are always valid, and which, if the (unknown) relaxation time of the chain is sufficiently small relative to $ m / n$, have length $ O(n^{-1} \log n)$ with high probability.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Confidence interval, Exact sampling, Markov chain Monte Carlo.", } @Article{Borovkov:2001:KIF, author = "Konstantin Borovkov and Zaeem Burq", title = "{Kendall}'s identity for the first crossing time revisited", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "9:91--9:94", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1038", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1038", abstract = "We give a new relatively compact proof of the famous identity for the distribution of the first hitting time of a linear boundary by a skip-free process with stationary independent increments. The proof uses martingale identities and change of measure.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Skip-free L{\'e}vy process, first crossing time, change of measure.", } @Article{Bertoin:2001:SSS, author = "Jean Bertoin and Marc Yor", title = "On Subordinators, Self-Similar {Markov} Processes and Some Factorizations of the Exponential Variable", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "10:95--10:106", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1039", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1039", abstract = "Let $ \xi $ be a subordinator with Laplace exponent $ \Phi $, $ I = \int_0^{\infty } \exp ( - \xi_s)d s $ the so-called exponential functional, and $X$ (respectively, $ \hat X$) the self-similar Markov process obtained from $ \xi $ (respectively, from $ \hat {\xi } = - \xi $) by Lamperti's transformation. We establish the existence of a unique probability measure $ \rho $ on $]0, \infty [$ with $k$-th moment given for every $ k \in N$ by the product $ \Phi (1) \cdots \Phi (k)$, and which bears some remarkable connections with the preceding variables. In particular we show that if $R$ is an independent random variable with law $ \rho $ then $ I R$ is a standard exponential variable, that the function $ t \to E(1 / X_t)$ coincides with the Laplace transform of $ \rho $, and that $ \rho $ is the $1$-invariant distribution of the sub-Markovian process $ \hat X$. A number of known factorizations of an exponential variable are shown to be of the preceding form $ I R$ for various subordinators $ \xi $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Self-similar Markov process, subordinator, exponential functional", } @Article{Konig:2001:ELP, author = "Wolfgang K{\"o}nig and Neil O'Connell", title = "Eigenvalues of the {Laguerre} Process as Non-Colliding Squared {Bessel} Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "11:107--11:114", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1040", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1040", abstract = "Let $ A(t) $ be an $ n \times p $ matrix with independent standard complex Brownian entries and set $ M(t) = A(t)^*A(t) $. This is a process version of the Laguerre ensemble and as such we shall refer to it as the {\em Laguerre process\/}. The purpose of this note is to remark that, assuming $ n > p $, the eigenvalues of $ M(t) $ evolve like $p$ independent squared Bessel processes of dimension $ 2 (n - p + 1)$, conditioned (in the sense of Doob) never to collide. More precisely, the function $ h(x) = \prod_{i < j}(x_i - x_j)$ is harmonic with respect to $p$ independent squared Bessel processes of dimension $ 2 (n - p + 1)$, and the eigenvalue process has the same law as the corresponding Doob $h$-transform. In the case where the entries of $ A(t)$ are {\em real\/} Brownian motions, $ (M(t))_{t > 0}$ is the Wishart process considered by Bru (1991). There it is shown that the eigenvalues of $ M(t)$ evolve according to a certain diffusion process, the generator of which is given explicitly. An interpretation in terms of non-colliding processes does not seem to be possible in this case. We also identify a class of processes (including Brownian motion, squared Bessel processes and generalised Ornstein--Uhlenbeck processes) which are all amenable to the same $h$-transform, and compute the corresponding transition densities and upper tail asymptotics for the first collision time.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Wishart and Laguerre ensembles and processes, eigenvalues as diffusions, non-colliding squared Bessel processes.", } @Article{Schramm:2001:PF, author = "Oded Schramm", title = "A Percolation Formula", journal = j-ELECTRON-COMMUN-PROBAB, volume = "6", pages = "12:115--12:120", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v6-1041", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1041", abstract = "Let $A$ be an arc on the boundary of the unit disk $U$. We prove an asymptotic formula for the probability that there is a percolation cluster $K$ for critical site percolation on the triangular grid in $U$ which intersects $A$ and such that $0$ is surrounded by the union of $K$ and $A$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "SLE, Cardy, conformal invariance", } @Article{OConnell:2001:RNC, author = "Neil O'Connell and Marc Yor", title = "A Representation for Non-Colliding Random Walks", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "1:1--1:12", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1042", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1042", abstract = "We define a sequence of mappings $ \Gamma_k : D_0 (R_+)^k \to D_0 (R_+)^k $ and prove the following result: Let $ N_1, \ldots, N_n $ be the counting functions of independent Poisson processes on $ R_+ $ with respective intensities $ \mu_1 < \mu_2 < \cdots < \mu_n $. The conditional law of $ N_1, \ldots, N_n $, given that\par $$ N_1 (t) \le \cdots \le N_n(t), \mbox { for all }t \ge 0, $$ is the same as the unconditional law of $ \Gamma_n(N) $. From this, we deduce the corresponding results for independent Poisson processes of equal rates and for independent Brownian motions (in both of these cases the conditioning is in the sense of Doob). This extends a recent observation, independently due to Baryshnikov (2001) and Gravner, Tracy and Widom (2001), which relates the law of a certain functional of Brownian motion to that of the largest eigenvalue of a GUE random matrix. Our main result can also be regarded as a generalisation of Pitman's representation for the 3-dimensional Bessel process.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "GUE, eigenvalues of random matrices, Hermitian Brownian motion, non-colliding Brownian motions, Weyl chamber, queues in series, Burke's theorem, reversibility, Pitman's representation theorem, Charlier ensemble.", } @Article{Alili:2001:CDC, author = "Larbi Alili", title = "Canonical Decompositions of Certain Generalized {Brownian} Bridges", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "3:27--3:35", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1044", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1044", abstract = "We define a generalized Brownian bridge and we provide some information about its filtration. Two decompositions of this process as a semi-martingale are given. The first one is a Volterra decomposition and the second one is its canonical decomposition in its own filtration.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian bridge; Brownian motion; Canonical decomposition; Volterra transform.", } @Article{Ressel:2001:SAU, author = "Paul Ressel", title = "Subdiagonal and Almost Uniform Distributions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "10:97--10:100", year = "2001", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1051", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1051", abstract = "A distribution (function) $F$ on $ [0, 1]$ with $ F(t)$ less or equal $t$ for all $t$ is called {\em subdiagonal\/}. The extreme subdiagonal distributions are identified as those whose distribution functions are almost surely the identity, or equivalently for which $ F \circ F = F$. There exists a close connection to exchangeable random orders on $ \{ 1, 2, 3, \ldots {} \} $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Subdiagonal distribution, almost uniform distribution, exchangeable random order.", } @Article{Feng:2002:LDQ, author = "Shui Feng and Jie Xiong", title = "Large Deviations and Quasi-Potential of a {Fleming--Viot} Process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "2:13--2:25", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1043", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1043", abstract = "The large deviation principle is established for the Fleming--Viot process with neutral mutation when the process starts from a point on the boundary. Since the diffusion coefficient is degenerate on the boundary, the boundary behavior of the process is investigated in detail. This leads to the explicit identification of the rate function, the quasi-potential, and the structure of the effective domain of the rate function.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Fleming--Viot process, large deviations, quasi-potential.", } @Article{Baudoin:2002:FEG, author = "Fabrice Baudoin", title = "Further Exponential Generalization of {Pitman}'s {$ 2 M - X $} Theorem", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "4:37--4:46", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1045", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1045", abstract = "We present a class of processes which enjoy an exponential analogue of Pitman's $ 2 M - X $ theorem, improving hence some works of H. Matsumoto and M. Yor.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Diffusion processes, Exponential analogue of Pitman's 2M-X theorem.", } @Article{Rempala:2002:APS, author = "Grzegorz Rempala and Jacek Wesolowski", title = "Asymptotics for Products of Sums and {$U$}-statistics", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "5:47--5:54", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1046", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1046", abstract = "The product of subsequent partial sums of independent, identically distributed, square integrable, positive random variables is asymptotically lognormal. The result extends in a rather routine way to non-degenerate $U$-statistics.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Central limit theorem, lognormal distribution, products of sums of iid rv's, records, $U$-statistics", } @Article{Panchenko:2002:SEI, author = "Dmitriy Panchenko", title = "Some Extensions of an Inequality of {Vapnik} and {Chervonenkis}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "6:55--6:65", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1047", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1047", abstract = "The inequality of Vapnik and Chervonenkis controls the expectation of the function by its sample\par average uniformly over a VC-major class of functions taking into account the size of the expectation.\par Using Talagrand's kernel method we prove a similar result for the classes of functions for which Dudley's\par uniform entropy integral or bracketing entropy integral is finite.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Concentration of measure, empirical processes", } @Article{Haggstrom:2002:MRH, author = "Olle H{\"a}ggstr{\"o}m", title = "A Monotonicity Result for Hard-core and {Widom--Rowlinson} Models on Certain $d$-dimensional Lattices", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "7:67--7:78", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1048", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1048", abstract = "For each $ d \geq 2 $, we give examples of $d$-dimensional periodic lattices on which the hard-core and Widom--Rowlinson models exhibit a phase transition which is monotonic, in the sense that there exists a critical value $ \lambda_c$ for the activity parameter $ \lambda $, such that there is a unique Gibbs measure (resp. multiple Gibbs measures) whenever $ \lambda $ is less than $ \lambda_c$ (resp. $ \lambda $ greater than $ \lambda_c$). This contrasts with earlier examples of such lattices, where the phase transition failed to be monotonic. The case of the cubic lattice $ Z^d$ remains an open problem.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Hard-core model, Widom--Rowlinson model, Gibbs measures, monotonic phase transition, site-random-cluster model.", } @Article{Klebaner:2002:OPW, author = "Fima Klebaner", title = "Option Price When the Stock is a Semimartingale", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "8:79--8:83", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1049", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1049", abstract = "The purpose of this note is to give a PDE satisfied by a call option when the price process is a semimartingale. The main result generalizes the PDE in the case when the stock price is a diffusion. Its proof uses Meyer-Tanaka and occupation density formulae. Presented approach also gives a new insight into the classical Black-Scholes formula. Rigorous proofs of some known results are also given.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Black-Scholes formula, Meyer-Tanaka formula, semimartingales.", } @Article{Kessler:2002:IER, author = "David Kessler and Jeremy Schiff", title = "{Inclusion-Exclusion} {{\em Redux}}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "9:85--9:96", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1050", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1050", abstract = "We present a reordered version of the inclusion--exclusion principle, which is useful when computing the probability of a union of events which are close to independent. The advantages of this formulation are demonstrated in the context of 3 classic problems in combinatorics.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Inclusion-exclusion principle, close-to-independent events.", } @Article{Boivin:2002:GRR, author = "Daniel Boivin and Jean-Marc Derrien", title = "Geodesics and Recurrence of Random Walks in Disordered Systems", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "11:101--11:115", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1052", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1052", abstract = "In a first-passage percolation model on the square lattice $ Z^2 $, if the passage times are independent then the number of geodesics is either $0$ or $ + \infty $. If the passage times are stationary, ergodic and have a finite moment of order $ \alpha > 1 / 2$, then the number of geodesics is either $0$ or $ + \infty $. We construct a model with stationary passage times such that $ E \lbrack t(e)^\alpha \rbrack < \infty $, for every $ 0 < \alpha < 1 / 2$, and with a unique geodesic. The recurrence/transience properties of reversible random walks in a random environment with stationary conductances $ (a(e); e$ is an edge of $ \mathbb {Z}^2)$ are considered.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Geodesics in first-passage percolation model; Random environment with stationary conductances; Recurrence and transience.; Reversible random walks on $Z^2$", } @Article{Soucaliuc:2002:NRB, author = "Florin Soucaliuc and Wendelin Werner", title = "A Note on Reflecting {Brownian} Motions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "12:117--12:122", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1053", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1053", abstract = "We give another proof of the following result from a joint paper with B{\'a}lint T{\'o}th: {\em A Brownian motion reflected on an independent time-reversed Brownian motion is a Brownian motion.}", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion, reflection", } @Article{Rosenthal:2002:QCR, author = "Jeffrey Rosenthal", title = "Quantitative Convergence Rates of {Markov} Chains: A Simple Account", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "13:123--13:128", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1054", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1054", abstract = "We state and prove a simple quantitative bound on the total variation distance after $k$ iterations between two Markov chains with different initial distributions but identical transition probabilities. The result is a simplified and improved version of the result in Rosenthal (1995), which also takes into account the $ \epsilon $-improvement of Roberts and Tweedie (1999), and which follows as a special case of the more complicated time-inhomogeneous results of Douc et al. (2002). However, the proof we present is very short and simple; and we feel that it is worthwhile to boil the proof down to its essence. This paper is purely expository; no new results are presented.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Markov chain, convergence rate, mixing time, drift condition, minorisation condition, total variation distance.", } @Article{Atar:2002:NLN, author = "Rami Atar and Krzysztof Burdzy", title = "On Nodal Lines of {Neumann} Eigenfunctions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "14:129--14:139", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1055", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1055", abstract = "We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Nodal line, reflected Brownian motion, mirror coupling, eigenfunction, Neumann problem", } @Article{Machida:2002:FAA, author = "Motoya Machida", title = "{Fill}'s Algorithm for Absolutely Continuous Stochastically Monotone Kernels", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "15:141--15:155", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1056", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1056", abstract = "Fill, Machida, Murdoch, and Rosenthal (2000) presented their algorithm and its variants to extend the perfect sampling algorithm of Fill (1998) to chains on continuous state spaces. We consider their algorithm for absolutely continuous stochastically monotone kernels, and show the correctness of the algorithm under a set of certain regularity conditions. These conditions succeed in relaxing the previously known hypotheses sufficient for their algorithm to apply.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Markov chain Monte Carlo, Fill's algorithm, perfect sampling, exact sampling, rejection sampling, stochastic monotonicity, partially ordered set, monotone coupling, absolutely continuous Markov kernel, regularity conditions.", } @Article{Wang:2002:SCC, author = "Hao Wang", title = "State Classification for a Class of Interacting Superprocesses with Location Dependent Branching", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "16:157--16:167", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1057", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1057", abstract = "The spatial structure of a class of superprocesses which arise as limits in distribution of a class of interacting particle systems with location dependent branching is investigated. The criterion of their state classification is obtained. Their effective state space is contained in the set of purely-atomic measures or the set of absolutely continuous measures according as one diffusive coefficient $ c(x) \equiv 0 $ or $ |c(x)| \geq \epsilon > 0 $ while another diffusive coefficient $ h \in C^2_b(R) $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "spatial structure, interaction, superprocess, location dependent branching", } @Article{Bahlali:2002:EUS, author = "Khaled Bahlali", title = "Existence and uniqueness of solutions for {BSDEs} with locally {Lipschitz} coefficient", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "17:169--17:179", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1058", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1058", abstract = "We deal with multidimensional backward stochastic differential equations (BSDE) with locally Lipschitz coefficient in both variables $ y, z $ and an only square integrable terminal data. Let $ L_N $ be the Lipschitz constant of the coefficient on the ball $ B(0, N) $ of $ R^d \times R^{dr} $. We prove that if $ L_N = O (\sqrt {\log N }) $, then the corresponding BSDE has a unique solution. Moreover, the stability of the solution is established under the same assumptions. In the case where the terminal data is bounded, we establish the existence and uniqueness of the solution also when the coefficient has an arbitrary growth (in $y$) and without restriction on the behaviour of the Lipschitz constant $ L_N $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Backward stochastic differential equations (BSDE), locally Lipschitz function.", } @Article{Griffin:2002:TSS, author = "Philip Griffin", title = "Tightness of the {Student} $t$-Statistic", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "18:181--18:190", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1059", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1059", abstract = "Let $ X, X_1, X_2, \dots $ be a sequence of nondegenerate, independent and identically distributed random variables and set $ S_n = X_1 + \dots + X_n $, $ V_n^2 = X_1^2 + \dots + X_n^2 $. We answer a question of Gotze, Gine and Mason by providing a simple necessary and sufficient condition for tightness of $ S_n / V_n $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "tightness, t-statistic, self-normalized sum", } @Article{Zerner:2002:NBL, author = "Martin Zerner", title = "A Non-Ballistic Law of Large Numbers for Random Walks in {I.I.D.} Random Environment", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "19:191--19:197", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1060", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1060", abstract = "We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general law of large numbers under the only assumption of a certain zero-one law, which is known to hold if the dimension is two.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random walk in random environment, RWRE, law of large numbers.", } @Article{Mikami:2002:OCA, author = "Toshio Mikami", title = "Optimal Control for Absolutely Continuous Stochastic Processes and the Mass Transportation Problem", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "20:199--20:213", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1061", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1061", abstract = "We study the optimal control problem for $ \mathbb {R}^d$-valued absolutely continuous stochastic processes with given marginal distributions at every time. When $ d = 1$, we show the existence and the uniqueness of a minimizer which is a function of a time and an initial point. When $ d > 1$, we show that a minimizer exists and that minimizers satisfy the same ordinary differential equation.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Absolutely continuous stochastic process, mass transportation problem, Salisbury's problem, Markov control, zero-noise limit", } @Article{vanZanten:2002:COM, author = "Harry van Zanten", title = "Continuous {Ocone} Martingales as Weak Limits of Rescaled Martingales", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "21:215--21:222", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1062", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", note = "See remark and counterexample \cite{Peccati:2004:WCO}.", URL = "http://ecp.ejpecp.org/article/view/1062", abstract = "Consider a martingale $M$ with bounded jumps and two sequences $ a_n, b_n \to \infty $. We show that if the rescaled martingales\par $$ M^n_t = \frac {1}{\sqrt {a_n}}M_{b_n t} $$ converge weakly, then the limit is necessarily a continuous Ocone martingale. Necessary and sufficient conditions for the weak convergence of the rescaled martingales are also given.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Appleby:2002:ASS, author = "John Appleby", title = "Almost Sure Stability of Linear {It{\^o}--Volterra} Equations with Damped Stochastic Perturbations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "7", pages = "22:223--22:234", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v7-1063", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1063", abstract = "In this paper we study the a.s. convergence of all solutions of the It{\^o}--Volterra equation $$ d X(t) = (A X(t) + \int_0^t K(t - s)X(s), d s) \, d t + \Sigma (t) \, d W(t) $$ to zero. $A$ is a constant $ d \times d$ matrix, $K$ is a $ d \times d$ continuous and integrable matrix function, $ \Sigma $ is a continuous $ d \times r$ matrix function, and $W$ is an $r$-dimensional Brownian motion. We show that when $$ x'(t) = A x(t) + \int_0^t K(t - s)x(s) \, d s $$ has a uniformly asymptotically stable zero solution, and the resolvent has a polynomial upper bound, then $X$ converges to 0 with probability 1, provided $$ \lim_{t \rightarrow \infty } | \Sigma (t)|^2 \log t = 0. $$ A converse result under a monotonicity restriction on $ | \Sigma |$ establishes that the rate of decay for $ | \Sigma |$ above is necessary. Equations with bounded delay and neutral equations are also considered.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stochastic functional-differential equations, It{\^o}--Volterra equations, uniform asymptotic stability, almost sure stability, pathwise stability, simulated annealing.", } @Article{Gao:2003:MML, author = "Fuchang Gao", title = "The Mean of a Maximum Likelihood Estimator Associated with the {Brownian} Bridge", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "1:1--1:5", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1064", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1064", abstract = "A closed formula for the mean of a maximum likelihood estimator associated with the Brownian bridge is obtained; the exact relation with that of the Brownian motion is established.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian bridge, intrinsic volume, solid angle", } @Article{Angel:2003:RWA, author = "Omer Angel and Itai Benjamini and B{\'a}lint Vir{\'a}g", title = "Random Walks that Avoid Their Past Convex Hull", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "2:6--2:16", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1065", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1065", abstract = "We explore planar random walk conditioned to avoid its past convex hull. We prove that it escapes at a positive lim sup speed. Experimental results show that fluctuations from a limiting direction are on the order of $ n^{3 / 4} $. This behavior is also observed for the extremal investor, a natural financial model related to the planar walk.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Holroyd:2003:TMP, author = "Alexander Holroyd and Yuval Peres", title = "Trees and Matchings from Point Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "3:17--3:27", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1066", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1066", abstract = "A {\em factor graph\/} of a point process is a graph whose vertices are the points of the process, and which is constructed from the process in a deterministic isometry-invariant way. We prove that the {\em d\/}-dimensional Poisson process has a one-ended tree as a factor graph. This implies that the Poisson points can be given an ordering isomorphic to the usual ordering of the integers in a deterministic isometry-invariant way. For $d$ greater than or equal to 4 our result answers a question posed by Ferrari, Landim and Thorisson [7]. We prove also that any isometry-invariant ergodic point process of finite intensity in Euclidean or hyperbolic space has a perfect matching as a factor graph provided all the inter-point distances are distinct.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Poisson process, point process, random tree, random matching, minimal spanning forest.", } @Article{Dubedat:2003:ST, author = "Julien Dub{\'e}dat", title = "{SLE} and Triangles", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "4:28--4:42", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1067", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1067", abstract = "By analogy with Carleson's observation on Cardy's formula describing crossing probabilities for the scaling limit of critical percolation, we exhibit ``privileged geometries'' for Stochastic Loewner Evolutions with various parameters, for which certain hitting distributions are uniformly distributed. We then examine consequences for limiting probabilities of events concerning various critical plane discrete models.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stochastic Loewner Evolution. FK percolation. Double domino tilings. Uniform spanning tree.", } @Article{Duheille-Bienvenue:2003:CLT, author = "Fr{\'e}d{\'e}rique Duheille-Bienvenue and Nadine Guillotin-Plantard", title = "{Central Limit Theorems} for the Products of Random Matrices Sampled by a Random Walk", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "5:43--5:50", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1068", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1068", abstract = "The purpose of the present paper is to study the asymptotic behaviour of the products of random matrices indexed by a random walk following the results obtained by Furstenberg and Kesten (MR53:14670) and by Ishitani (MR 53:14670).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random Walk, Random Matrix, Random Scenery, Functional limit theorem", } @Article{Gobet:2003:CGB, author = "Emmanuel Gobet and Arturo Kohatsu-Higa", title = "Computation of {Greeks} for Barrier and Lookback Options Using {Malliavin} Calculus", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "6:51--6:62", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1069", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1069", abstract = "In this article, we consider the numerical computations associated to the Greeks of barrier and lookback options, using Malliavin calculus. For this, we derive some integration by parts formulae involving the maximum and minimum of a one dimensional diffusion. Numerical tests illustrate the gain of accuracy compared to classical methods.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Barrier and lookback options. Option sensitivities. Malliavin calculus.", } @Article{Sepanski:2003:LIL, author = "Steven Sepanski", title = "A Law of the Iterated Logarithm for the Sample Covariance Matrix", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "7:63--7:76", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1070", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1070", abstract = "For a sequence of independent identically distributed Euclidean random vectors, we prove a law of the iterated logarithm for the sample covariance matrix when {\em o(log log n) \/}terms are omitted. The result is proved under the hypothesis that the random vectors belong to the generalized domain of attraction of the multivariate Gaussian law. As an application, we obtain a bounded law of the iterated logarithm for the multivariate t-statistic.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "law of the iterated logarithm, sample covariance, central limit theorem, generalized domain of attraction, multivariate t statistic, extreme values, operator normalization, self normalization", } @Article{Wilson:2003:MTR, author = "David Wilson", title = "Mixing Time of the {Rudvalis} Shuffle", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "8:77--8:85", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1071", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1071", abstract = "We extend a technique for lower-bounding the mixing time of card-shuffling Markov chains, and use it to bound the mixing time of the Rudvalis Markov chain, as well as two variants considered by Diaconis and Saloff-Coste. We show that in each case $ \Theta (n^3 \log n) $ shuffles are required for the permutation to randomize, which matches (up to constants) previously known upper bounds. In contrast, for the two variants, the mixing time of an individual card is only $ \Theta (n^2) $ shuffles.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Markov chain, card shuffling, mixing time", } @Article{Benjamini:2003:ERW, author = "Itai Benjamini and David Wilson", title = "Excited Random Walk", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "9:86--9:92", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1072", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1072", abstract = "A random walk on $ \mathbb {Z}^d $ is excited if the first time it visits a vertex there is a bias in one direction, but on subsequent visits to that vertex the walker picks a neighbor uniformly at random. We show that excited random walk on $ \mathbb {Z}^d $ is transient iff $ d > 1 $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Perturbed random walk, transience", } @Article{Tracy:2003:SDE, author = "Craig Tracy and Harold Widom", title = "A System of Differential Equations for the {Airy} Process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "10:93--10:98", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1074", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1074", abstract = "The Airy process is characterized by its $m$-dimensional distribution functions. For $ m = 1$ it is known that this distribution function is expressible in terms of a solution to Painleve II. We show that each finite-dimensional distribution function is expressible in terms of a solution to a system of differential equations.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Airy process. Extended Airy kernel. Growth processes. Integrable differential equations.", } @Article{Weininger:2003:PCI, author = "Nicholas Weininger", title = "Positive correlation for increasing events with disjoint dependencies does not imply positive correlation for all increasing events", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "11:99--11:101", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1078", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1078", abstract = "A probability measure $ \mu $ on the lattice $ 2^{[n]} $ is said to be positively associated if any two increasing functions on the lattice are positively correlated with respect to $ \mu $. Pemantle asked whether, in order to establish positive association for a given mu, it might be sufficient to show positive correlation only for pairs of functions which depend on disjoint subsets of the ground set $ [n] $. We answer Pemantle's question in the negative, by exhibiting a measure which gives positive correlation for pairs satisfying Pemantle's condition but not for general pairs of increasing functions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Zaidi:2003:SLS, author = "Noureddine Za{\"\i}di and David Nualart", title = "Smoothness of the law of the supremum of the fractional {Brownian} motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "12:102--12:111", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1079", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1079", abstract = "This note is devoted to prove that the supremum of a fractional Brownian motion with Hurst parameter $ H \in \left (0, 1 \right) $ has an infinitely differentiable density on $ \left (0, \infty \right) $. The proof of this result is based on the techniques of the Malliavin calculus.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Malliavin calculus, fractional Brownian motion, fractional calculus", } @Article{Katori:2003:NBM, author = "Makoto Katori and Hideki Tanemura", title = "Noncolliding {Brownian} motions and {Harish-Chandra} formula", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "13:112--13:121", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1076", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1076", abstract = "We consider a system of noncolliding Brownian motions introduced in our previous paper, in which the noncolliding condition is imposed in a finite time interval $ (0, T] $. This is a temporally inhomogeneous diffusion process whose transition probability density depends on a value of $T$, and in the limit $ T \to \infty $ it converges to a temporally homogeneous diffusion process called Dyson's model of Brownian motions. It is known that the distribution of particle positions in Dyson's model coincides with that of eigenvalues of a Hermitian matrix-valued process, whose entries are independent Brownian motions. In the present paper we construct such a Hermitian matrix-valued process, whose entries are sums of Brownian motions and Brownian bridges given independently of each other, that its eigenvalues are identically distributed with the particle positions of our temporally inhomogeneous system of noncolliding Brownian motions. As a corollary of this identification we derive the Harish-Chandra formula for an integral over the unitary group.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "random matrices, Dyson's Brownian motion, Imhof's relation, Harish-Chandra formula.", } @Article{Boufoussi:2003:SDF, author = "Brahim Boufoussi and Youssef Ouknine", title = "On a {SDE} driven by a fractional {Brownian} motion and with monotone drift", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "14:122--14:134", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1084", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1084", abstract = "Let $ {B_t^H, t \in \lbrack 0, T]} $ be a fractional Brownian motion with Hurst parameter $ H > \frac {1}{2} $. We prove the existence of a weak solution for a stochastic differential equation of the form $ X_t = x + B_t^H + \int_0^t \left (b_1 (s, X_s) + b_2 (s, X_s) \right) d s $, where $ b_1 (s, x) $ is a Holder continuous function of order strictly larger than $ 1 - \frac {1}{2H} $ in $x$ and than $ H - \frac {1}{2}$ in time and $ b_2$ is a real bounded nondecreasing and left (or right) continuous function.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Fractional Brownian motion, Stochastic integrals, Girsanov transform", } @Article{Lalley:2003:SCL, author = "Steven Lalley", title = "Strict Convexity of the Limit Shape in First-Passage Percolation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "15:135--15:141", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1089", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1089", abstract = "Sufficient conditions are given for the strict convexity of the limit shape in standard first-passage percolation. These conditions involve (1) asymptotic ``straightness'' of the geodesics, and (2) existence of mean-zero limit distributions for the first-passage times.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Revelle:2003:HKA, author = "David Revelle", title = "Heat Kernel Asymptotics on the Lamplighter Group", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "16:142--16:154", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1092", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1092", abstract = "We show that, for one generating set, the on-diagonal decay of the heat kernel on the lamplighter group is asymptotic to $ c_1 n^{1 / 6} \exp [ - c_2 n^{1 / 3}] $. We also make off-diagonal estimates which show that there is a sharp threshold for which elements have transition probabilities that are comparable to the return probability. The off-diagonal estimates also give an upper bound for the heat kernel that is uniformly summable in time. The methods used also apply to a one dimensional trapping problem, and we compute the distribution of the walk conditioned on survival as well as a corrected asymptotic for the survival probability. Conditioned on survival, the position of the walker is shown to be concentrated within $ \alpha n^{1 / 3} $ of the origin for a suitable $ \alpha $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Bertoin:2003:PTF, author = "Jean Bertoin and Loic Chaumont and Jim Pitman", title = "Path transformations of first passage bridges", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "17:155--17:166", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1096", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1096", abstract = "We define the first passage bridge from 0 to $ \lambda $ as the Brownian motion on the time interval $ [0, 1] $ conditioned to first hit $ \lambda $ at time 1. We show that this process may be related to the Brownian bridge, the Bessel bridge or the Brownian excursion via some path transformations, the main one being an extension of Vervaat's transformation. We also propose an extension of these results to certain bridges with cyclically exchangeable increments.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Lugosi:2003:NRC, author = "G{\'a}bor Lugosi and Shahar Mendelson and Vladimir Koltchinskii", title = "A note on the richness of convex hulls of {VC} classes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "18:167--18:169", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1097", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1097", abstract = "We prove the existence of a class $A$ of subsets of $ \mathbb {R}^d$ of VC dimension 1 such that the symmetric convex hull $F$ of the class of characteristic functions of sets in $A$ is rich in the following sense. For any absolutely continuous probability measure $ \mu $ on $ \mathbb {R}^d$, measurable set $B$ and $ \varepsilon > 0$, there exists a function $f$ in $F$ such that the measure of the symmetric difference of $B$ and the set where $f$ is positive is less than $ \varepsilon $. The question was motivated by the investigation of the theoretical properties of certain algorithms in machine learning.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Guiol:2003:MSD, author = "Herve Guiol and Krishnamurthi Ravishankar and Ellen Saada", title = "Microscopic structure of a decreasing shock for the asymmetric $k$-step exclusion process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "19:170--19:178", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1080", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1080", abstract = "The asymmetric $k$-step exclusion processes are the simplest interacting particle systems whose hydrodynamic equation may exhibit both increasing and decreasing entropic shocks under Euler scaling. We prove that, under Riemann initial condition with right density zero and adequate left density, the rightmost particle identifies microscopically the decreasing shock.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Asymmetric k-step exclusion process, Non-convex or non-concave flux, microscopic shock, rightmost particle", } @Article{Kovchegov:2003:LSL, author = "Yevgeniy Kovchegov and Scott Sheffield", title = "Linear Speed Large Deviations for Percolation Clusters", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "20:179--20:183", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1098", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1098", abstract = "Let $ C_n $ be the origin-containing cluster in subcritical percolation on the lattice $ \frac {1}{n} \mathbb Z^d $, viewed as a random variable in the space $ \Omega $ of compact, connected, origin-containing subsets of $ \mathbb R^d $, endowed with the Hausdorff metric $ \delta $. When $ d \geq 2 $, and $ \Gamma $ is any open subset of $ \Omega $, we prove that\par $$ \lim_{n \rightarrow \infty } \frac {1}{n} \log P(C_n \in \Gamma) = - \inf_{S \in \Gamma } \lambda (S) $$ where $ \lambda (S) $ is the one-dimensional Hausdorff measure of $S$ defined using the {\em correlation norm\/}:\par $$ ||u|| := \lim_{n \rightarrow \infty } - \frac {1}{n} \log P (u_n \in C_n) $$ where $ u_n$ is $u$ rounded to the nearest element of $ \frac {1}{n} \mathbb Z^d$. Given points $ a^1, \ldots, a^k \in \mathbb R^d$, there are finitely many correlation-norm Steiner trees spanning these points and the origin. We show that if the $ C_n$ are each conditioned to contain the points $ a^1_n, \ldots, a^k_n$, then the probability that $ C_n$ fails to approximate one of these trees tends to zero exponentially in $n$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Kahn:2003:ITC, author = "Jeff Kahn", title = "Inequality of Two Critical Probabilities for Percolation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "8", pages = "21:184--21:187", year = "2003", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v8-1099", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1099", abstract = "We disprove a conjecture of Russ Lyons---that for every locally finite, connected graph $G$, the critical probability for (Bernoulli bond) percolation on $G$ is equal to the {"first} moment {method"} lower bound on this probability---and propose a possible alternative.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Londono:2004:STN, author = "Jaime Londono", title = "State Tameness: A New Approach for Credit Constrains", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "1:1--1:13", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1102", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1102", abstract = "We propose a new definition for tameness within the model of security prices as It{\^o} processes that is risk-aware. We give a new definition for arbitrage and characterize it. We then prove a theorem that can be seen as an extension of the second fundamental theorem of asset pricing, and a theorem for valuation of contingent claims of the American type. The valuation of European contingent claims and American contingent claims that we obtain does not require the full range of the volatility matrix. The technique used to prove the theorem on valuation of American contingent claims does not depend on the Doob-Meyer decomposition of super-martingales; its proof is constructive and suggest and alternative way to find approximations of stopping times that are close to optimal.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Csaki:2004:IPR, author = "Endre Csaki and Yueyun Hu", title = "Invariance Principles for Ranked Excursion Lengths and Heights", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "2:14--2:21", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1103", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1103", abstract = "In this note we prove strong invariance principles between ranked excursion lengths and heights of a simple random walk and those of a standard Brownian motion. Some consequences concerning limiting distributions and strong limit theorems will also be presented.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Birkner:2004:CWD, author = "Matthias Birkner", title = "A Condition for Weak Disorder for Directed Polymers in Random Environment", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "3:22--3:25", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1104", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1104", abstract = "We give a sufficient criterion for the weak disorder regime of directed polymers in random environment, which extends a well-known second moment criterion. We use a stochastic representation of the size-biased law of the partition function.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Hara:2004:FDD, author = "Keisuke Hara", title = "Finite dimensional determinants as characteristic functions of quadratic {Wiener} functionals", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "4:26--4:35", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1091", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1091", abstract = "We show a method and the structure to calculate the characteristic functions of quadratic Wiener functionals by using classical Weierstrass-Hadamard's theory on entire functions. We also examine the idea by an example for Gaussian processes with multiple Markovian property.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "entire functions; generalized determinants; quadratic Wiener functionals", } @Article{Xiong:2004:LTB, author = "Jie Xiong", title = "Long-term behavior for superprocesses over a stochastic flow", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "5:36--5:52", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1081", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1081", abstract = "We study the limit of a superprocess controlled by a stochastic flow as $ t \to \infty $. It is proved that when $ d \le 2 $, this process suffers long-time local extinction; when $ d \ge 3 $, it has a limit which is persistent. The stochastic log-Laplace equation conjectured by Skoulakis and Adler (2001) and studied by this author (2004) plays a key role in the proofs like the one played by the log-Laplace equation in deriving long-term behavior for usual super-Brownian motion.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Superprocess, stochastic flow, log-Laplace equation, long-term behavior.", } @Article{Timar:2004:TGF, author = "Adam Timar", title = "Tree and Grid factors of General Point processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "6:53--6:59", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1073", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1073", abstract = "We study isomorphism invariant point processes of $ R^d $ whose groups of symmetries are almost surely trivial. We define a 1-ended, locally finite tree factor on the points of the process, that is, a mapping of the point configuration to a graph on it that is measurable and equivariant with the point process. This answers a question of Holroyd and Peres. The tree will be used to construct a factor isomorphic to $ Z^n $. This perhaps surprising result (that any $d$ and $n$ works) solves a problem by Steve Evans. The construction, based on a connected clumping with $ 2^i$ vertices in each clump of the $i$'th partition, can be used to define various other factors.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "factors; Point Processes; random grid; random tree", } @Article{Biggins:2004:LDM, author = "J. D. Biggins", title = "Large Deviations for Mixtures", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "7:60--7:71", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1106", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1106", abstract = "The results discussed here are most easily described in words using Bayesian terminology. For each $n$, there are probability distributions for the data conditional on a parameter, and there is also a prior distribution for the parameter. Integrating out, using the prior, gives the (unconditional) distribution for the data, for each $n$. The question considered here is when large deviation principles for the conditional distributions and for the prior distributions imply a large deviation principle for the unconditional distributions. Chaganty (1997) also considered this question, but under stronger assumptions. The treatment here follows that of Dinwoodie and Zabell (1992) who, motivated by exchangeability, considered the case where the prior does not vary with $n$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Krishnapur:2004:RGW, author = "Manjunath Krishnapur and Yuval Peres", title = "Recurrent Graphs where Two Independent Random Walks Collide Finitely Often", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "8:72--8:81", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1111", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1111", abstract = "We present a class of graphs where simple random walk is recurrent, yet two independent walkers meet only finitely many times almost surely. In particular, the comb lattice, obtained from $ Z^2 $ by removing all horizontal edges off the $x$-axis, has this property. We also conjecture that the same property holds for some other graphs, including the incipient infinite cluster for critical percolation in $ Z^2$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Soshnikov:2004:PSL, author = "Alexander Soshnikov", title = "{Poisson} Statistics for the Largest Eigenvalues of {Wigner} Random Matrices with Heavy Tails", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "9:82--9:91", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1112", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1112", abstract = "We study large Wigner random matrices in the case when the marginal distributions of matrix entries have heavy tails. We prove that the largest eigenvalues of such matrices have Poisson", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Burdzy:2004:GO, author = "Krzysztof Burdzy and David White", title = "A {Gaussian} Oscillator", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "10:92--10:95", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1113", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1113", abstract = "We present a stochastic process with sawtooth paths whose distribution is given by a simple rule and whose stationary distribution is Gaussian. The process arose in a natural way in research on interaction of an inert particle with a Brownian particle.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Song:2004:SBG, author = "Renming Song and Zoran Vondracek", title = "Sharp Bounds for {Green} and Jumping Functions of Subordinate Killed {Brownian} Motions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "11:96--11:105", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1114", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1114", abstract = "In this paper we obtain sharp bounds for the Green function and jumping function of a subordinate killed Brownian motion in a bounded $ C^{1, 1} $ domain, where the subordinating process is a subordinator whose Laplace exponent has certain asymptotic behavior at infinity.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Appleby:2004:ONO, author = "John Appleby and Conall Kelly", title = "Oscillation and Non-oscillation in Solutions of Nonlinear Stochastic Delay Differential Equations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "12:106--12:118", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1115", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1115", abstract = "This paper studies the oscillation and nonoscillation of solutions of a nonlinear stochastic delay differential equation, where the noise perturbation depends on the current state, and the drift depends on a delayed argument. When the restoring force towards equilibrium is relatively strong, all solutions oscillate, almost surely. However, if the restoring force is superlinear, positive solutions exist with positive probability, and for suitably chosen initial conditions, the probability of positive solutions can be made arbitrarily close to unity.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Louis:2004:EPE, author = "Pierre-Yves Louis", title = "Ergodicity of {PCA}: Equivalence between Spatial and Temporal Mixing Conditions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "13:119--13:131", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1116", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1116", abstract = "For a general attractive Probabilistic Cellular Automata on $ S^{\mathbb {Z}^d} $, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition ($ \mathcal {A}$). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on $ \{ - 1; + 1 \}^{\mathbb {Z}^d}$ with a naturally associated Gibbsian potential $ \varphi $, we prove that a (spatial-) weak mixing condition ($ \mathcal {WM}$) for $ \varphi $ implies the validity of the assumption ($ \mathcal {A}$); thus {\em exponential (time-) ergodicity\/} of these dynamics towards the unique Gibbs measure associated to $ \varphi $ holds. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Jonasson:2004:OSR, author = "Johan Jonasson", title = "On the optimal strategy in a random game", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "14:132--14:139", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1100", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1100", abstract = "Consider a two-person zero-sum game played on a random $n$ by $n$ matrix where the entries are iid normal random variables. Let $Z$ be the number of rows in the support of the optimal strategy for player I given the realization of the matrix. (The optimal strategy is a.s. unique and $Z$ a.s. coincides with the number of columns of the support of the optimal strategy for player II.) Faris an Maier (see the references) make simulations that suggest that as $n$ gets large $Z$ has a distribution close to binomial with parameters $n$ and 1/2 and prove that $ P(Z = n) < 2^{-(k - 1)}$. In this paper a few more theoretically rigorous steps are taken towards the limiting distribution of $Z$: It is shown that there exists $ a < 1 / 2$ (indeed $ a < 0.4$) such that $ P((1 / 2 - a)n < Z < (1 / 2 + a)n)$ tends to 1 as $n$ increases. It is also shown that the expectation of $Z$ is $ (1 / 2 + o(1))n$. We also prove that the value of the game with probability $ 1 - o(1)$ is at most $ C n^{-1 / 2}$ for some finite $C$ independent of $n$. The proof suggests that an upper bound is in fact given by $ f(n) / n$, where $ f(n)$ is any sequence tending to infinity as $n$ increases, and it is pointed out that if this is true, then the variance of $Z$ is $ o(n^2)$ so that any $ a > 0$ will do in the bound on $Z$ above.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "two-person game, mixed strategy, equalizing strategy, saddle point", } @Article{Kendall:2004:GEP, author = "Wilfrid Kendall", title = "Geometric Ergodicity and Perfect Simulation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "15:140--15:151", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1117", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1117", abstract = "This note extends the work of Foss and Tweedie (1998), who showed that availability of the classic Coupling from the Past (CFTP) algorithm of Propp and Wilson (1996) is essentially equivalent to uniform ergodicity for a Markov chain (see also Hobert and Robert, 2004). In this note we show that all geometrically ergodic chains possess dominated CFTP algorithms (not necessarily practical!) which are rather closely connected to Foster-Lyapunov criteria. Hence geometric ergodicity implies dominated CFTP.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Jarai:2004:BDH, author = "Antal Jarai and Harry Kesten", title = "A Bound for the Distribution of the Hitting Time of Arbitrary Sets by Random Walk", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "16:152--16:161", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1119", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1119", abstract = "We consider a random walk $ S_n = \sum_{i = 1}^n X_i $ with i.i.d. $ X_i $. We assume that the $ X_i $ take values in $ \mathbb {Z^d} $, have bounded support and zero mean. For $ A \subset \mathbb {Z^d}, A \ne \emptyset $ we define $ \tau_A = \inf {n \ge 0 : S_n \in A} $. We prove that there exists a constant $C$, depending on the common distribution of the $ X_i$ and $d$ only, such that $ \sup_{\emptyset \ne A \subset \mathbb {Z^d}} P \{ \tau_A = n \} \le C / n, n \ge 1$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Gine:2004:SNC, author = "Evarist Gin{\'e} and Friedrich G{\"o}tze", title = "On Standard Normal Convergence of the Multivariate {Student} $t$-Statistic for Symmetric Random Vectors", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "17:162--17:171", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1120", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1120", abstract = "It is proved that if the multivariate Student $t$-statistic based on i.i.d. symmetric random vectors is asymptotically standard normal, then these random vectors are in the generalized domain of attraction of the normal law. Uniform integrability is also considered, even in the absence of symmetry.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Peccati:2004:WCO, author = "Giovanni Peccati", title = "Weak Convergence to {Ocone} Martingales: a Remark", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "18:172--18:174", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1121", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", note = "See \cite{vanZanten:2002:COM}.", URL = "http://ecp.ejpecp.org/article/view/1121", abstract = "We show, by a simple counterexample, that the main result in a recent paper by H. Van Zanten [Electronic Communications in Probability {\bf 7} (2002), 215--222] is false. We eventually point out the origin of the error.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Friedli:2004:LRP, author = "Sacha Friedli and Beno{\^\i}te Borge de Lima and Vladas Sidoravicius", title = "On Long Range Percolation with Heavy Tails", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "19:175--19:177", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1122", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1122", abstract = "Consider independent long range percolation on $ \mathbf {Z}^d $, $ d \geq 2 $, where edges of length $n$ are open with probability $ p_n$. We show that if $ \limsup_{n \to \infty }p_n > 0, $ then there exists an integer $N$ such that $ P_N(0 \leftrightarrow \infty) > 0$, where $ P_N$ is the truncated measure obtained by taking $ p_{N, n} = p_n$ for $ n \leq N$ and $ p_{N, n} = 0$ for all $ n > N$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Janson:2004:CMI, author = "Svante Janson and Philippe Chassaing", title = "The Center of Mass of the {ISE} and the {Wiener} Index of Trees", journal = j-ELECTRON-COMMUN-PROBAB, volume = "9", pages = "20:178--20:187", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v9-1088", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1088", abstract = "We derive the distribution of the center of mass S of the integrated superBrownian excursion (ISE) from the asymptotic distribution of the Wiener index for simple trees. Equivalently, this is the distribution of the integral of a Brownian snake. A recursion formula for the moments and asymptotics for moments and tail probabilities are derived.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian excursion; Brownian snake; center of mass; ISE; Wiener index", } @Article{Morandin:2005:RBP, author = "Francesco Morandin", title = "A Resummed Branching Process Representation for a Class of Nonlinear ODEs", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "1:1--1:6", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1126", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1126", abstract = "We study some probabilistic representations, based on branching processes, of a simple nonlinear differential equation, i.e. $ u' = \lambda u(a u^R - 1) $. The first approach is basically the same used by Le Jan and Sznitman for 3-d Navier--Stokes equations, which need small initial data to work. In our much simpler setting we are able to make this precise, finding all the cases where their method fails to give the solution. The second approach is based on a resummed representation, which we can prove to give all the solutions of the problem, even those with large initial data.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Barbato:2005:FIB, author = "David Barbato", title = "{FKG} Inequality for {Brownian} Motion and Stochastic Differential Equations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "2:7--2:16", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1127", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1127", abstract = "The purpose of this work is to study some possible application of FKG inequality to the Brownian motion and to Stochastic Differential Equations. We introduce a special ordering on the Wiener space and prove the FKG inequality with respect to this ordering. Then we apply this result on the solutions $ X_t $ of a stochastic differential equation with a positive coefficient $ \sigma $ , we prove that these solutions $ X_t $ are increasing with respect to the ordering, and finally we deduce a correlation inequality between the solution of different stochastic equations.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Manstavicius:2005:NMP, author = "Martynas Manstavicius", title = "A Non-{Markovian} Process with Unbounded $p$-Variation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "3:17--3:28", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1128", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1128", abstract = "A recent theorem by M. Manstavicius (2004) provided a link between a certain function of transition probabilities of a strong Markov process and the boundedness of the $p$-variation of its trajectories. Here one assumption of that theorem is relaxed and an example is constructed to show that the Markov property cannot be easily dispensed with.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Marchal:2005:MCS, author = "Philippe Marchal", title = "Measure Concentration for Stable Laws with Index Close to 2", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "4:29--4:35", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1129", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1129", abstract = "We give upper bounds for the probability $ P(|f(X) - E f(X)| > x) $, where $X$ is a stable random variable with index close to 2 and $f$ is a Lipschitz function. While the optimal upper bound is known to be of order $ 1 / x^\alpha $ for large $x$, we establish, for smaller $x$, an upper bound of order $ \exp ( - x^\alpha / 2)$, which relates the result to the Gaussian concentration.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Rassoul-Agha:2005:ZOL, author = "Firas Rassoul-Agha", title = "On the Zero--One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "5:36--5:44", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1130", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1130", abstract = "We prove a weak version of the law of large numbers for multi-dimensional finite range random walks in certain mixing elliptic random environments. This already improves previously existing results, where a law of large numbers was known only under strong enough transience. We also prove that for such walks the zero-one law implies a law of large numbers.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Hammond:2005:CEP, author = "Alan Hammond", title = "Critical Exponents in Percolation via Lattice Animals", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "6:45--6:59", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1131", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1131", abstract = "We examine the percolation model on $ \mathbb {Z}^d $ by an approach involving lattice animals and their surface-area-to-volume ratio. For $ \beta \in [0, 2 (d - 1)) $, let $ f(\beta) $ be the asymptotic exponential rate in the number of edges of the number of lattice animals containing the origin which have surface-area-to-volume ratio $ \beta $. The function $f$ is bounded above by a function which may be written in an explicit form. For low values of $ \beta $ ($ \beta \leq 1 / p_c - 1$), equality holds, as originally demonstrated by F. Delyon. For higher values ($ \beta > 1 / p_c - 1$), the inequality is strict.\par We introduce two critical exponents, one of which describes how quickly $f$ falls away from the explicit form as $ \beta $ rises from $ 1 / p_c - 1$, and the second of which describes how large clusters appear in the marginally subcritical regime of the percolation model. We demonstrate that the pair of exponents must satisfy certain inequalities. Other such inequalities yield sufficient conditions for the absence of an infinite cluster at the critical value (c.f. {citetechrep}). The first exponent is related to one of a more conventional nature in the scaling theory of percolation, that of correlation size. In deriving this relation, we find that there are two possible behaviours, depending on the value of the first exponent, for the typical surface-area-to-volume ratio of an unusually large cluster in the marginally subcritical regime.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Ball:2005:PTM, author = "Karen Ball", title = "{Poisson} Thinning by Monotone Factors", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "7:60--7:69", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1134", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1134", abstract = "Let $X$ and $Y$ be Poisson point processes on the real numbers with rates $ l_1$ and $ l_2$ respectively. We show that if $ l_1 > l_2$, then there exists a deterministic map $f$ such that $ f(X)$ and $Y$ have the same distribution, the joint distribution of $ (X, f(X))$ is translation-invariant, and which is monotone in the sense that for all intervals $I$, $ f(X)(I) \leq X(I)$, almost surely.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Mason:2005:WDR, author = "David Mason and Joel Zinn", title = "When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "8:70--8:81", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1135", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", note = "See acknowledgment of priority \cite{Mason:2005:APW}.", URL = "http://ecp.ejpecp.org/article/view/1135", abstract = "We determine exactly when a certain randomly weighted, self--normalized sum converges in distribution, partially verifying a 1965 conjecture of Leo Breiman. We, then, apply our results to characterize the asymptotic distribution of relative sums and to provide a short proof of a 1973 conjecture of Logan, Mallows, Rice and Shepp on the asymptotic distribution of self--normalized sums in the case of symmetry.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Carlsson:2005:SNT, author = "Niclas Carlsson", title = "Some Notes on Topological Recurrence", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "9:82--9:93", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1137", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1137", abstract = "We review the concept of topological recurrence for weak Feller Markov chains on compact state spaces and explore the implications of this concept for the ergodicity of the processes. We also prove some conditions for existence and uniqueness of invariant measures of certain types. Examples are given from the class of iterated function systems on the real line.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Kozlova:2005:NOT, author = "Marina Kozlova and Paavo Salminen", title = "A Note on Occupation Times of Stationary Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "10:94--10:104", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1138", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1138", abstract = "Consider a real valued stationary process $ X = {X_s :, s \in R} $. For a fixed $ t \in R $ and a set $D$ in the state space of $X$, let $ g_t$ and $ d_t$ denote the starting and the ending time, respectively, of an excursion from and to $D$ (straddling $t$). Introduce also the occupation times $ I^+_t$ and $ I^-_t$ above and below, respectively, the observed level at time $t$ during such an excursion. In this note we show that the pairs $ (I^+_t, I^-_t)$ and $ (t - g_t, d_t - t)$ are identically distributed. This somewhat curious property is, in fact, seen to be a fairly simple consequence of the known general uniform sojourn law which implies that conditionally on $ I^+_t + I^-_t = v$ the variable $ I^+_t$ (and also $ I^-_t$) is uniformly distributed on $ (0, v)$. We also particularize to the stationary diffusion case and show, e.g., that the distribution of $ I^-_t + I^+_t$ is a mixture of gamma distributions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Bodineau:2005:UPL, author = "Thierry Bodineau and James Martin", title = "A Universality Property for Last-Passage Percolation Paths Close to the Axis", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "11:105--11:112", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1139", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1139", abstract = "We consider a last-passage directed percolation model in $ Z_+^2 $, with i.i.d. weights whose common distribution has a finite $ (2 + p) $ th moment. We study the fluctuations of the passage time from the origin to the point $ (n, n^a) $. We show that, for suitable $a$ (depending on $p$), this quantity, appropriately scaled, converges in distribution as $ n \to \infty $ to the Tracy-Widom distribution, irrespective of the underlying weight distribution. The argument uses a coupling to a Brownian directed percolation problem and the strong approximation of Koml{\'o}s, Major and Tusn{\'a}dy.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Kordzakhia:2005:EMH, author = "George Kordzakhia", title = "The Escape Model on a Homogeneous Tree", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "12:113--12:124", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1140", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1140", abstract = "There are two types of particles interacting on a homogeneous tree of degree $ d + 1 $. The particles of the first type colonize the empty space with exponential rate 1, but cannot take over the vertices that are occupied by the second type. The particles of the second type spread with exponential rate $ \lambda $. They colonize the neighboring vertices that are either vacant or occupied by the representatives of the opposite type, and annihilate the particles of the type 1 as they reach them. There exists a critical value $ \lambda_c = (2 d - 1) + \sqrt {(2d - 1)^2 - 1} $ such that the first type survives with positive probability for $ \lambda < \lambda_c $, and dies out with probability one for $ \lambda > \lambda_c $. We also find the growth profile which characterizes the rate of growth of the type 1 in the space-time on the event of survival.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Conlon:2005:HND, author = "Joseph Conlon and Ian Pilizzotto", title = "On Homogenization of Non-Divergence Form Partial Difference Equations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "13:125--13:135", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1141", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1141", abstract = "In this paper a method for proving homogenization of divergence form elliptic equations is extended to the non-divergence case. A new proof of homogenization is given when the coefficients in the equation are assumed to be stationary and ergodic. A rate of convergence theorem in homogenization is also obtained, under the assumption that the coefficients are i.i.d. and the elliptic equation can be solved by a convergent perturbation series.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Hobson:2005:DBC, author = "Tim Hobson and Rodge Tribe", title = "On the Duality between Coalescing {Brownian} Particles and the Heat Equation Driven by {Fisher--Wright} Noise", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "14:136--14:145", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1143", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1143", abstract = "This paper concerns the Markov process duality between the one-dimensional heat equation driven by Fisher-Wright white noise and slowly coalescing Brownian particles. A representation is found for the law of the solution $ x \to U(t, x) $ to the stochastic PDE, at a fixed time, in terms of a labelled system of such particles.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Kyprianou:2005:NSO, author = "Andreas Kyprianou and Budhi Surya", title = "On the {Novikov--Shiryaev} Optimal Stopping Problems in Continuous Time", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "15:146--15:154", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1144", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1144", abstract = "Novikov and Shiryaev (2004) give explicit solutions to a class of optimal stopping problems for random walks based on other similar examples given in Darling et al. (1972). We give the analogue of their results when the random walk is replaced by a L{\'e}vy process. Further we show that the solutions show no contradiction with the conjecture given in Alili and Kyprianou (2004) that there is smooth pasting at the optimal boundary if and only if the boundary of the stopping region is irregular for the interior of the stopping region.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Panchenko:2005:QAP, author = "Dmitriy Panchenko", title = "A Question about the {Parisi} Functional", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "16:155--16:166", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1145", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1145", abstract = "We conjecture that the Parisi functional in the SK model is convex in the functional order parameter and prove a partial result that shows the convexity along one-sided directions. A consequence of this result is the log-convexity of $ L_m $ norm for a class or random variables.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Angel:2005:JPB, author = "Omer Angel and Alexander Holroyd and James Martin", title = "The Jammed Phase of the {Biham--Middleton--Levine} Traffic Model", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "17:167--17:178", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1148", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1148", abstract = "Initially a car is placed with probability $p$ at each site of the two-dimensional integer lattice. Each car is equally likely to be East-facing or North-facing, and different sites receive independent assignments. At odd time steps, each North-facing car moves one unit North if there is a vacant site for it to move into. At even time steps, East-facing cars move East in the same way. We prove that when $p$ is sufficiently close to 1 traffic is jammed, in the sense that no car moves infinitely many times. The result extends to several variant settings, including a model with cars moving at random times, and higher dimensions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Caravenna:2005:CAB, author = "Francesco Caravenna and Giambattista Giacomin", title = "On Constrained Annealed Bounds for Pinning and Wetting Models", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "18:179--18:189", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1150", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1150", abstract = "The free energy of quenched disordered systems is bounded above by the free energy of the corresponding annealed system. This bound may be improved by applying the annealing procedure, which is just Jensen inequality, after having modified the Hamiltonian in a way that the quenched expressions are left unchanged. This procedure is often viewed as a partial annealing or as a constrained annealing, in the sense that the term that is added may be interpreted as a Lagrange multiplier on the disorder variables.\par In this note we point out that, for a family of models, some of which have attracted much attention, the multipliers of the form of empirical averages of local functions cannot improve on the basic annealed bound from the viewpoint of characterizing the phase diagram. This class of multipliers is the one that is suitable for computations and it is often believed that in this class one can approximate arbitrarily well the quenched free energy.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Catuogno:2005:GSD, author = "Pedro Catuogno and Paulo Ruffino", title = "Geometry of Stochastic Delay Differential Equations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "19:190--19:195", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1151", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1151", abstract = "Stochastic delay differential equations (SDDE) on a manifold $M$ depend intrinsically on a connection $ \nabla $ in this space. The main geometric result in this notes concerns the horizontal lift of solutions of SDDE on a manifold $M$ to an SDDE in the frame bundle $ B M$, hence the lifted equation should come together with the prolonged horizontal connection $ \nabla^H$ on $ B M$. We show that every horizontal semimartingale can be represented as a solution of an SDDE.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Khoshnevisan:2005:EVA, author = "Davar Khoshnevisan and David Levin and Zhan Shi", title = "An Extreme-Value Analysis of the {LIL} for {Brownian} Motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "20:196--20:206", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1154", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1154", abstract = "We use excursion theory and the ergodic theorem to present an extreme-value analysis of the classical law of the iterated logarithm (LIL) for Brownian motion. A simplified version of our method also proves, in a paragraph, the classical theorem of Darling and Erd{\H{o}}s (1956).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Hashorva:2005:BCB, author = "Enkelejd Hashorva", title = "Boundary Crossings of {Brownian} Motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "21:207--21:217", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1155", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1155", abstract = "Let $B$ be a standard Brownian motion and let $ b_\gamma $ be a piecewise linear continuous boundary function. In this paper we obtain an exact asymptotic expansion of $ P \{ B(t) < b_\gamma (t), \forall t \in [0, 1] \} $ provided that the boundary function satisfies $ \lim_{\gamma \to \infty } b_\gamma (t^*) = - \infty $ for some $ t^* \in (0, 1]$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Chobanyan:2005:SLL, author = "Sergei Chobanyan and Shlomo Levental and Habib Salehi", title = "Strong Law of Large Numbers Under a General Moment Condition", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "22:218--22:222", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1156", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1156", abstract = "We use our maximum inequality for $p$-th order random variables ($ p > 1$) to prove a strong law of large numbers (SLLN) for sequences of $p$-th order random variables. In particular, in the case $ p = 2$ our result shows that $ \sum f(k) / k < \infty $ is a sufficient condition for SLLN for $f$-quasi-stationary sequences. It was known that the above condition, under the additional assumption of monotonicity of $f$, implies SLLN (Erdos (1949), Gal and Koksma (1950), Gaposhkin (1977), Moricz (1977)). Besides getting rid of the monotonicity condition, the inequality enables us to extend the general result to $p$-th order random variables, as well as to the case of Banach-space-valued random variables.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Handa:2005:SFS, author = "Kenji Handa", title = "Sampling Formulae for Symmetric Selection", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "23:223--23:234", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1159", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1159", abstract = "We study partition distributions in a population genetics model incorporating symmetric selection and mutation. They generalize Ewens distributions in the infinitely-many-neutral-alleles model, an explicit expression of which is known as the Ewens sampling formula. A sampling formula for the generalized model is obtained by means of calculus for Poisson and gamma processes.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Liao:2005:MRB, author = "Ming Liao and Longmin Wang", title = "Motion of a Rigid Body under Random Perturbation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "24:235--24:243", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1163", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1163", abstract = "We use stochastic analysis to study the random motion of a rigid body under a white noise perturbation. We obtain a formula for the angular velocity in an average sense and discuss the stability near a principle axis.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Roitershtein:2005:LSL, author = "Alexander Roitershtein", title = "A Log-scale Limit Theorem for One-dimensional Random Walks in Random Environments", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "25:244--25:253", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1164", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1164", abstract = "We consider a transient one-dimensional random walk $ X_n $ in random environment having zero asymptotic speed. For a class of non-i.i.d. environments we show that $ \log X_n / \log n $ converges in probability to a positive constant.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Istas:2005:SHF, author = "Jacques Istas", title = "Spherical and Hyperbolic Fractional {Brownian} Motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "26:254--26:262", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1166", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1166", abstract = "We define a Fractional Brownian Motion indexed by a sphere, or more generally by a compact rank one symmetric space, and prove that it exists if, and only if, $ 0 < H \leq 1 / 2 $. We then prove that Fractional Brownian Motion indexed by an hyperbolic space exists if, and only if, $ 0 < H \leq 1 / 2 $. At last, we prove that Fractional Brownian Motion indexed by a real tree exists when $ 0 < H \leq 1 / 2 $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Popov:2005:RWA, author = "Serguei Popov and Marina Vachkovskaia", title = "Random Walk Attracted by Percolation Clusters", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "27:263--27:272", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1167", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1167", abstract = "Starting with a percolation model in $ \mathbb {Z}^d $ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$. This function is supposed to be increasing, so that the random walk is attracted by bigger clusters. For $ f(t) = e^{\beta t}$ we prove that there is a phase transition in $ \beta $, i.e., the random walk is subdiffusive for large $ \beta $ and is diffusive for small $ \beta $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Khan:2005:LLR, author = "T{\"a}mur Khan and Luc Devroye and Ralph Neininger", title = "A Limit Law for the Root Value of Minimax Trees", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "28:273--28:281", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1168", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1168", abstract = "We consider minimax trees with independent, identically distributed leaf values that have a continuous distribution function $ F_V $ being strictly increasing on the range where $ 0 < F_V < 1 $. It was shown by Pearl that the root value of such trees converges to a deterministic limit in probability without any scaling. We show that after normalization we have convergence in distribution to a nondegenerate limit random variable.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Roch:2005:BFM, author = "S{\'e}bastien Roch", title = "Bounding Fastest Mixing", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "29:282--29:296", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1169", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1169", abstract = "In a recent work, Boyd, Diaconis and Xiao introduced a semidefinite programming approach for computing the fastest mixing Markov chain on a graph of allowed transitions, given a target stationary distribution. In this paper, we show that standard mixing time analysis techniques---variational characterizations, conductance, canonical paths---can be used to give simple, nontrivial lower and upper bounds on the fastest mixing time. To test the applicability of this idea, we consider several detailed examples including the Glauber dynamics of the Ising model.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Mason:2005:APW, author = "David Mason and Joel Zinn", title = "Acknowledgment of Priority: {When Does a Randomly Weighted Self-normalized Sum Converge in Distribution? (\booktitle{Elect. Comm. in Probab.} {\bf 10} (2005), 70--81)}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "10", pages = "30:297--30:297", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v10-1170", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", note = "See \cite{Mason:2005:WDR}.", URL = "http://ecp.ejpecp.org/article/view/1170", abstract = "Christian Houdre has kindly pointed us to a paper by A. Fuks, A. Joffe and J. Teugels, where their Theorem 5.3 is our Proposition 3 in the case $ 0 < \alpha < 1 $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Taniguchi:2006:QWF, author = "Setsuo Taniguchi", title = "On the Quadratic {Wiener} Functional Associated with the {Malliavin} Derivative of the Square Norm of {Brownian} Sample Path on Interval", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "1:1--1:10", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1174", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1174", abstract = "Exact expressions of the stochastic oscillatory integrals with the phase function, which is the quadratic Wiener functional obtained from the Malliavin derivative of the square norm of the Brownian sample path on interval, are given. As an application, the density function of the distribution of the half of the Wiener functional is given.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Balan:2006:SAM, author = "Raluca Balan and Ingrid-Mona Zamfirescu", title = "Strong Approximation for Mixing Sequences with Infinite Variance", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "2:11--2:23", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1175", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1175", abstract = "In this paper we prove a strong approximation result for a mixing sequence with infinite variance and logarithmic decay rate of the mixing coefficient. The result is proved under the assumption that the distribution is symmetric and lies in the domain of attraction of the normal law. Moreover the truncated variance function is supposed to be slowly varying with log-log type remainder.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Gaans:2006:IMS, author = "Onno Gaans and Jan Neerven", title = "Invariant measures for stochastic {Cauchy} problems with asymptotically unstable drift semigroup", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "3:24--3:34", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1184", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1184", abstract = "We investigate existence and permanence properties of invariant measures for abstract stochastic Cauchy problems of the form\par $$ d U(t) = (A U(t) + f) \, d t + B \, d W_H(t), \ \ t \ge 0, $$ governed by the generator $A$ of an asymptotically unstable $ C_0$-semigroup on a Banach space $E$. Here $ f \in E$ is fixed, $ W_H$ is a cylindrical Brownian motion over a separable real Hilbert space $H$, and $B$ is a bounded operator from $H$ to $E$. We show that if $E$ does not contain a copy of $ c_0$, such invariant measures fail to exist generically but may exist for a dense set of operators $B$. It turns out that many results on invariant measures which hold under the assumption of uniform exponential stability of $S$ break down without this assumption.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Invariant measures, stochastic evolution equations in Hilbert spaces", } @Article{Dacunha-Castelle:2006:DLM, author = "Didier Dacunha-Castelle and Lisandro Fermin", title = "Disaggregation of Long Memory Processes on $ \mathcal {C}^{\infty } $ Class", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "4:35--4:44", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1133", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1133", abstract = "We prove that a large set of long memory (LM) processes (including classical LM processes and all processes whose spectral densities have a countable number of singularities controlled by exponential functions) are obtained by an aggregation procedure involving short memory (SM) processes whose spectral densities are infinitely differentiable ($ C^\infty $). We show that the $ C^\infty $ class of spectral densities infinitely differentiable is the best class to get a general result for disaggregation of LM processes in SM processes, in the sense that the result given in $ C^\infty $ class cannot be improved by taking for instance analytic functions instead of indefinitely derivable functions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Aggregation; disaggregation; long memory process; mixture.", } @Article{Kontoyiannis:2006:MCC, author = "Ioannis Kontoyiannis and Mokshay Madiman", title = "Measure Concentration for Compound {Poisson} Distributions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "5:45--5:57", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1190", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1190", abstract = "We give a simple development of the concentration properties of compound Poisson measures on the nonnegative integers. A new modification of the Herbst argument is applied to an appropriate modified logarithmic-Sobolev inequality to derive new concentration bounds. When the measure of interest does not have finite exponential moments, these bounds exhibit optimal {em polynomial} decay. Simple new proofs are also given for earlier results of Houdr{\'e} (2002) and Wu (2000).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Compound Poisson measure; entropy method; Herbst argument; logarithmic-Sobolev inequality; measure concentration; polynomial tails", } @Article{Andrew:2006:PFP, author = "Peter Andrew", title = "A Proof from `First Principles' of {Kesten}'s Result for the Probabilities with which a Subordinator Hits Points", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "6:58--6:63", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1193", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1193", abstract = "We give a simpler and shorter proof of Kesten's result for the probabilities with which a subordinator hits points.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "L{\'e}vy processes, subordinators, hitting probabilities", } @Article{Gozlan:2006:ICT, author = "Nathael Gozlan", title = "Integral criteria for transportation cost inequalities", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "7:64--7:77", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1198", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1198", abstract = "Abstract. In this paper, we provide a characterization of a large class of transportation-cost inequalities in terms of exponential integrability of the cost function under the reference probability measure. Our results completely extend the previous works by Djellout, Guillin and Wu (DGW03) and Bolley and Villani (BV03).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Transportation-cost inequalities and Orlicz Spaces", } @Article{Andersson:2006:VFN, author = "Jenny Andersson and Olle H{\"a}ggstr{\"o}m and Marianne M{\aa}nsson", title = "The volume fraction of a non-overlapping germ--grain model", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "8:78--8:88", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1197", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1197", abstract = "We discuss the volume fraction of a model of non-overlapping convex grains. It is obtained from thinning a Poisson process where each point has a weight and is the centre of a grain, by removing any grain that is overlapped by one of larger or equal weight. In the limit as the intensity of the Poisson process tends to infinity, the model can be identified with the intact grains in the dead leaves model if the weights are independent of the grain sizes. In this case we can show that the volume fraction is at most $ 1 / 2^d $ for $ d = 1 $ or $2$ if the shape is fixed, but the size and the orientation are random. The upper bound is achieved for centrally symmetric sets of the same size and orientation. For general $d$ we can show the upper bound, $ 1 / 2^d$, for spherical grains with two--point radius distribution. If dependence between weight and size is allowed, it is possible to achieve a volume fraction arbitrarily close to one.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "volume fraction, germ-grain model, dead leaves model", } @Article{Weerasinghe:2006:CSG, author = "Ananda Weerasinghe", title = "A Controller And A Stopper Game With Degenerate Variance Control", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "9:89--9:99", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1202", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1202", abstract = "We consider a zero sum stochastic differential game which involves two players, {\em the controller\/} and {\em the stopper}. The stopper selects the stopping rule which halts the game. The controller chooses the diffusion coefficient of the corresponding state process which is allowed to degenerate. At the end of the game, the controller pays the stopper, the amount $ E \int_0^{\tau } e^{- \alpha t} C(Z_x(t))d t $, where $ Z_x(\cdot) $ represents the state process with initial position $x$ and $ \alpha $ is a positive constant. Here $ C(\cdot)$ is a reward function where the set $ \{ x : C(x) > 0 \} $ is an open interval which contains the origin. Under some assumptions on the reward function $ C(\cdot)$ and the drift coefficient of the state process, we show that this game has a value. Furthermore, this value function is Lipschitz continuous, but it fails to be a $ C^1$ function.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "stochastic games, optimal stopping, degenerate diffusions, saddle point", } @Article{Benjamini:2006:RWW, author = "Itai Benjamini and Gady Kozma and Dan Romik", title = "Random walks with $k$-wise independent increments", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "10:100--10:107", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1201", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1201", abstract = "We construct examples of a random walk with pairwise-independent steps which is almost surely bounded, and for any m and k a random walk with k-wise independent steps which has no stationary distribution modulo m.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "pairwise independence; pseudo-randomness; quasi-randomness; Random walk", } @Article{Khoshnevisan:2006:NFP, author = "Davar Khoshnevisan and Paavo Salminen and Marc Yor", title = "A note on a.s. finiteness of perpetual integral functionals of diffusions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "11:108--11:117", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1203", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1203", abstract = "In this note we use the boundary classification of diffusions in order to derive a criterion for the convergence of perpetual integral functionals of transient real-valued diffusions. We present a second approach, based on Khas'minskii's lemma, which is applicable also to spectrally negative L{\'e}vy processes. In the particular case of transient Bessel processes, our criterion agrees with the one obtained via Jeulin's convergence lemma.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion, random time change, exit boundary, local time, additive functional, stochastic differential equation, Khas'minskii's lemma, spectrally negative L{\'e}vy process.", } @Article{Zerner:2006:RTE, author = "Martin Zerner", title = "Recurrence and transience of excited random walks on {$ Z^d $} and strips", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "12:118--12:128", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1200", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1200", abstract = "We investigate excited random walks on $ Z^d, d \ge 1, $ and on planar strips $ Z \times {0, 1, \ldots, L - 1} $ which have a drift in a given direction. The strength of the drift may depend on a random i.i.d. environment and on the local time of the walk. We give exact criteria for recurrence and transience, thus generalizing results by Benjamini and Wilson for once-excited random walk on $ Z^d $ and by the author for multi-excited random walk on $Z$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Excited Random Walk, Recurrence, Self-Interacting Random Walk, Transience", } @Article{Chigansky:2006:RPF, author = "Pavel Chigansky and Robert Liptser", title = "On a role of predictor in the filtering stability", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "13:129--13:140", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1205", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1205", abstract = "When is a nonlinear filter stable with respect to its initial condition? In spite of the recent progress, this question still lacks a complete answer in general. Currently available results indicate that stability of the filter depends on the signal ergodic properties and the observation process regularity and may fail if either of the ingredients is ignored. In this note we address the question of stability in a particular weak sense and show that the estimates of certain functions are always stable. This is verified without dealing directly with the filtering equation and turns to be inherited from certain one-step predictor estimates.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "nonlinear filtering, stability, martingale convergence", } @Article{Nicolas:2006:SSC, author = "Fournier Nicolas", title = "Standard stochastic coalescence with sum kernels", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "14:141--14:148", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1206", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1206", abstract = "We build a Markovian system of particles entirely characterized by their masses, in which each pair of particles with masses $x$ and $y$ coalesce at rate $ K(x, y) \simeq x^\lambda + y^\lambda $, for some $ \lambda \in (0, 1)$, and such that the system is initially composed of infinitesimally small particles.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Coalescence, Stochastic interacting particle systems", } @Article{Dembo:2006:LMD, author = "Amir Dembo and Qi-Man Shao", title = "Large and Moderate Deviations for {Hotelling}'s {$ T^2 $}-Statistics", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "15:149--15:159", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1209", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1209", abstract = "Let $ \mathbf {X}, \mathbf {X}_1, \mathbf {X}_2, \ldots {} $ be i.i.d. $ \mathbb {R}^d$-valued random variables. We prove large and moderate deviations for Hotelling's $ T^2$-statistic when $ \mathbf {X}$ is in the generalized domain of attraction of the normal law.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "$T^2$ statistic; large deviation; law of the iterated logarithm; moderate deviation; self-normalized partial sums", } @Article{Pimentel:2006:TCC, author = "Leandro Pimentel", title = "The time constant and critical probabilities in percolation models", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "16:160--16:167", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1210", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1210", abstract = "We consider a first-passage percolation (FPP) model on a Delaunay triangulation $ \mathcal {D} $ of the plane. In this model each edge $ \mathbf {e} $ of $ \mathcal {D} $ is independently equipped with a nonnegative random variable $ \tau_{\mathbf {e}} $, with distribution function $ \mathbb {F} $, which is interpreted as the time it takes to traverse the edge. Vahidi-Asl and Wierman \cite{VW90} have shown that, under a suitable moment condition on $ \mathbb {F} $, the minimum time taken to reach a point $ \mathbf {x} $ from the origin $ \mathbf {0} $ is asymptotically $ \mu (\mathbb {F})| \mathbf {x}| $, where $ \mu (\mathbb {F}) $ is a nonnegative finite constant. However the exact value of the time constant $ \mu (\mathbb {F}) $ still a fundamental problem in percolation theory. Here we prove that if $ \mathbb {F}(0) < 1 - p_c^* $ then $ \mu (\mathbb {F}) > 0 $, where $ p_c^* $ is a critical probability for bond percolation on the dual graph $ \mathcal {D}^* $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "critical probabilities; Delaunay triangulations; Percolation; time constant", } @Article{Steif:2006:SRP, author = "Jeffrey Steif and Aidan Sudbury", title = "Some results for poisoning in a catalytic model", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "17:168--17:177", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1211", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1211", abstract = "We obtain new results concerning poisoning\slash nonpoisoning in a catalytic model which has previously been introduced and studied. We show that poisoning can occur even when the arrival rate of one gas is smaller than the sum of the arrival rates of the other gases, and that poisoning does not occur when all gases have equal arrival rates.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Interacting particle systems, catalytic model.", } @Article{Bass:2006:PUR, author = "Richard Bass and Krzysztof Burdzy", title = "Pathwise uniqueness for reflecting {Brownian} motion in certain planar {Lipschitz} domains", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "18:178--18:181", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1213", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1213", abstract = "We give a simple proof that in a Lipschitz domain in two dimensions with Lipschitz constant one, there is pathwise uniqueness for the Skorokhod equation governing reflecting Brownian motion.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "reflecting Brownian motion", } @Article{Vadlamani:2006:GGU, author = "Sreekar Vadlamani and Robert Adler", title = "Global geometry under isotropic {Brownian} flows", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "19:182--19:192", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1212", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1212", abstract = "We consider global properties of a codimension one manifold embedded in Euclidean space, as it evolves under an isotropic and volume preserving Brownian flow of diffeomorphisms. In particular, we obtain expressions describing the expected rate of growth of the Lipschitz-Killing curvatures, or intrinsic volumes, of the manifold under the flow. These results shed new light on some of the intriguing growth properties of flows from a global perspective, rather than the local perspective, on which there is a much larger literature.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian flows; evolution equations; Lipschitz-Killing curvatures; Lyapunov exponents.; manifolds; Stochastic flows", } @Article{deLaFortelle:2006:SFL, author = "Arnaud {de La Fortelle}", title = "{Yule} Process sample path asymptotics", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "20:193--20:199", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1215", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1215", abstract = "This paper presents two results on sample paths for the Yule process: one fluid limit theorem and one sample path large deviation result. The main interest is to understand the way large deviation occurs in the case of non-homogeneous processes. There are indeed two new phenomena. First there is no ``typical'' speed of large deviation. Second, the large deviation event is concentrated on a finite interval of time.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Large deviations, random trees, branching process, fluid limit, Yule process, martingale, change of measure", } @Article{Kuelske:2006:SFL, author = "Christof Kuelske and Enza Orlandi", title = "A simple fluctuation lower bound for a disordered massless random continuous spin model in $ d = 2 $", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "21:200--21:205", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1218", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1218", abstract = "We prove a finite volume lower bound of the order $ \sqrt {\log N} $ on the delocalization of a disordered continuous spin model (resp. effective interface model) in $ d = 2 $ in a box of size $N$. The interaction is assumed to be massless, possibly anharmonic and dominated from above by a Gaussian. Disorder is entering via a linear source term. For this model delocalization with the same rate is proved to take place already without disorder. We provide a bound that is uniform in the configuration of the disorder, and so our proof shows that disorder will only enhance fluctuations.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Interfaces, quenched systems, continuous spin models, entropy inequality", } @Article{Tevzadze:2006:EME, author = "Revaz Tevzadze and Mikhael Mania", title = "An Exponential Martingale Equation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "22:206--22:216", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1220", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1220", abstract = "We prove an existence of a unique solution of an exponential martingale equation in the class of BMO martingales. The solution is used to characterize optimal martingale measures.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Backward stochastic differential equation, exponential martingale, martingale measures", } @Article{Yang:2006:SPH, author = "Ming Yang", title = "A short proof of the {Hausdorff} dimension formula for {L{\'e}vy} processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "23:217--23:219", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1199", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1199", abstract = "A different but very short proof of a recent result of Khoshnevisan.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Hausdorff dimension", } @Article{Major:2006:MVH, author = "Peter Major", title = "A multivariate version of {Hoeffding}'s inequality", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "24:220--24:229", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1221", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1221", abstract = "In this paper a multivariate version of Hoeffding's inequality is proved about the tail distribution of homogeneous polynomials of Rademacher functions with an optimal constant in the exponent of the upper bound. The proof is based on an estimate about the moments of homogeneous polynomials of Rademacher functions which can be considered as an improvement of Borell's inequality in a most important special case.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Hoeffding's inequality, Borell's inequality, multiple Wiener--It{\^o} integrals, diagram formula", } @Article{Fitzsimmons:2006:ERE, author = "Patrick Fitzsimmons", title = "On the Existence of Recurrent Extensions of Self-similar {Markov} Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "25:230--25:241", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1222", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1222", abstract = "Let $ X = (X_t)_{t \geq 0} $ be a self-similar Markov process with values in the non-negative half-line, such that the state $0$ is a trap. We present a necessary and sufficient condition for the existence of a self-similar recurrent extension of $X$ that leaves $0$ continuously. This condition is expressed in terms of the L{\'e}vy process associated with $X$ by the Lamperti transformation.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "self-similar, semi-stable, Lamperti transformation, recurrent extension, Cram{\'e}r condition, excursion", } @Article{Istas:2006:FFI, author = "Jacques Istas", title = "On Fractional Fields indexed by Metric Spaces", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "26:242--26:251", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1223", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1223", abstract = "We define and build $H$-fractional $ \alpha $-stable fields indexed by a metric space $ (E, d)$. We mainly apply these results to spheres, hyperbolic spaces and real trees.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Fractional Stable Fields, Metric Spaces", } @Article{LeGall:2006:OMS, author = "Jean-Fran{\c{c}}ois {Le Gall} and Mathieu Merle", title = "On the occupation measure of super-{Brownian} motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "27:252--27:265", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1225", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1225", abstract = "We derive the asymptotic behavior of the total occupation measure of the unit ball for super-Brownian motion started from the Dirac measure at a distant point and conditioned to hit the unit ball. In the critical dimension 4, we obtain a limiting exponential distribution.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "super-Brownian motion, occupation measure, limit distribution", } @Article{Rueschendorf:2006:ETB, author = "Ludger Rueschendorf and Eva-Maria Schopp", title = "Exponential tail bounds for max-recursive sequences", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "28:266--28:277", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1227", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1227", abstract = "Exponential tail bounds are derived for solutions of max-recursive equations and for max-recursive random sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algorithms. In particular they arise in the worst case analysis of divide and conquer algorithms, in parallel search algorithms or in the height of random tree models. For the proof we determine asymptotic bounds for the moments or for the Laplace transforms and apply a characterization of exponential tail bounds due to Kasahara (1978).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "recursive algorithm, exponential bounds, divide and conquer algorithm, probabilistic analysis of algorithms", } @Article{Evans:2006:ENZ, author = "Steven Evans", title = "The expected number of zeros of a random system of $p$-adic polynomials", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "29:278--29:290", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1230", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1230", abstract = "We study the simultaneous zeros of a random family of $d$ polynomials in $d$ variables over the $p$-adic numbers. For a family of natural models, we obtain an explicit constant for the expected number of zeros that lie in the $d$-fold Cartesian product of the $p$-adic integers. Considering models in which the maximum degree that each variable appears is $N$, this expected value is\par $$ p^{d \lfloor \log_p N \rfloor } \left (1 + p^{-1} + p^{-2} + \cdots + p^{-d} \right)^{-1} $$ for the simplest such model.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "co-area formula, Kac-Rice formula, local field, Gaussian, $q$-binomial formula, random matrix", } @Article{Kondo:2006:SPE, author = "Hitoshi Kondo and Makoto Maejima and Ken-iti Sato", title = "Some properties of exponential integrals of {L{\'e}vy} processes and examples", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "30:291--30:303", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1232", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1232", abstract = "The improper stochastic integral $ Z = \int_0^{\infty -} \exp ( - X_{s-})d Y_s $ is studied, where $ { (X_t, Y_t), t \geq 0 } $ is a L{\'e}vy process on $ R^{1 + d} $ with $ {X_t } $ and $ {Y_t } $ being $R$-valued and $ R^d$-valued, respectively. The condition for existence and finiteness of $Z$ is given and then the law $ {\cal L}(Z)$ of $Z$ is considered. Some sufficient conditions for $ {\cal L}(Z)$ to be selfdecomposable and some sufficient conditions for $ {\cal L}(Z)$ to be non-selfdecomposable but semi-selfdecomposable are given. Attention is paid to the case where $ d = 1$, $ {X_t}$ is a Poisson process, and $ {X_t}$ and $ {Y_t}$ are independent. An example of $Z$ of type $G$ with selfdecomposable mixing distribution is given", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Generalized Ornstein--Uhlenbeck process, L{\'e}vy process, selfdecomposability, semi-selfdecomposability, stochastic integral", } @Article{Duerre:2006:UMD, author = "Maximilian Duerre", title = "Uniqueness of multi-dimensional infinite volume self-organized critical forest-fire models", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "31:304--31:315", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1229", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1229", abstract = "In a forest-fire model, each site of the square lattice is either vacant or occupied by a tree. Vacant sites get occupied according to independent rate 1 Poisson processes. Independently at each site ignition occurs according to independent rate lambda Poisson processes. When a site is hit by ignition, then its whole occupied cluster becomes vacant instantaneously. The article studies whether a multi-dimensional infinite volume forest-fire process with given parameter is unique. Under an assumption on the decay of the cluster size distribution, a process that dominates the forest-fire process is used to show uniqueness. If lambda is big enough, then subcritical site percolation shows the correctness of the assumption", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "adapted; forest-fire model; forest-fires; self-organized criticality; unique", } @Article{Alabert:2006:LSD, author = "Aureli Alabert and Marco Ferrante", title = "Linear stochastic differential-algebraic equations with constant coefficients", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "32:316--32:335", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1236", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1236", abstract = "We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stochastic differential-algebraic equations, Random distributions", } @Article{Deijfen:2006:SRG, author = "Maria Deijfen and Johan Jonasson", title = "Stationary random graphs on {$Z$} with prescribed iid degrees and finite mean connections", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "33:336--33:346", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1239", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1239", abstract = "Let $F$ be a probability distribution with support on the non-negative integers. A model is proposed for generating stationary simple graphs on $Z$ with degree distribution $F$ and it is shown for this model that the expected total length of all edges at a given vertex is finite if $F$ has finite second moment. It is not hard to see that any stationary model for generating simple graphs on $Z$ will give infinite mean for the total edge length per vertex if $F$ does not have finite second moment. Hence, finite second moment of $F$ is a necessary and sufficient condition for the existence of a model with finite mean total edge length.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "degree distribution; Random graphs; stationary model", } @Article{Hildebrand:2006:CDG, author = "Martin Hildebrand", title = "On the {Chung--Diaconis--Graham} random process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "11", pages = "34:347--34:356", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v11-1237", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1237", abstract = "Chung, Diaconis, and Graham considered random processes of the form $ X_{n + 1} = 2 X_n + b_n \pmod p $ where $ X_0 = 0 $, $p$ is odd, and $ b_n$ for $ n = 0, 1, 2, \dots $ are i.i.d. random variables on $ \{ - 1, 0, 1 \} $. If $ \Pr (b_n = - 1) = \Pr (b_n = 1) = \beta $ and $ \Pr (b_n = 0) = 1 - 2 \beta $, they asked which value of $ \beta $ makes $ X_n$ get close to uniformly distributed on the integers mod $p$ the slowest. In this paper, we extend the results of Chung, Diaconis, and Graham in the case $ p = 2^t - 1$ to show that for $ 0 < \beta \le 1 / 2$, there is no such value of $ \beta $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random processes, discrete Fourier analysis", } @Article{Rokhlin:2007:MSP, author = "Dmitry Rokhlin", title = "Martingale selection problem and asset pricing in finite discrete time", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "1:1--1:8", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1240", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1240", abstract = "Given a set-valued stochastic process $ (V_t)_{t = 0}^T $, we say that the martingale selection problem is solvable if there exists an adapted sequence of selectors $ \xi_t \in V_t $, admitting an equivalent martingale measure. The aim of this note is to underline the connection between this problem and the problems of asset pricing in general discrete-time market models with portfolio constraints and transaction costs. For the case of relatively open convex sets $ V_t(\omega) $ we present effective necessary and sufficient conditions for the solvability of a suitably generalized martingale selection problem. We show that this result allows to obtain computationally feasible formulas for the price bounds of contingent claims. For the case of currency markets we also sketch a new proof of the first fundamental theorem of asset pricing.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "martingale selection, arbitrage, price bounds, constraints, transaction costs", } @Article{Lageraas:2007:PMC, author = "Andreas Lager{\aa}s", title = "A population model for {$ \Lambda $}-coalescents with neutral mutations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "2:9--2:20", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1245", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1245", abstract = "Bertoin and Le Gall (2003) introduced a certain probability measure valued Markov process that describes the evolution of a population, such that a sample from this population would exhibit a genealogy given by the so-called $ \Lambda $-coalescent, or coalescent with multiple collisions, introduced independently by Pitman (1999) and Sagitov (1999). We show how this process can be extended to the case where lineages can experience mutations. Regenerative compositions enter naturally into this model, which is somewhat surprising, considering a negative result by M{\"o}hle (2007).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "coalescent; exchangeability; mutations; population model; sampling formula", } @Article{Bose:2007:SNR, author = "Arup Bose and Arnab Sen", title = "Spectral norm of random large dimensional noncentral {Toeplitz} and {Hankel} matrices", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "3:21--3:27", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1243", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1243", abstract = "Suppose $ s_n $ is the spectral norm of either the Toeplitz or the Hankel matrix whose entries come from an i.i.d. sequence of random variables with positive mean $ \mu $ and finite fourth moment. We show that $ n^{-1 / 2}(s_n - n \mu) $ converges to the normal distribution in either case. This behaviour is in contrast to the known result for the Wigner matrices where $ s_n - n \mu $ is itself asymptotically normal.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Large dimensional random matrix, eigenvalues, Wigner matrix, Toeplitz matrix, Hankel matrix, spectral norm.", } @Article{Iksanov:2007:PPW, author = "Alex Iksanov and Martin M{\"o}hle", title = "A probabilistic proof of a weak limit law for the number of cuts needed to isolate the root of a random recursive tree", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "4:28--4:35", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1253", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1253", abstract = "We present a short probabilistic proof of a weak convergence result for the number of cuts needed to isolate the root of a random recursive tree. The proof is based on a coupling related to a certain random walk.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "coupling; random recursive tree; random walk; stable limit", } @Article{Kargin:2007:PNC, author = "Vladislav Kargin", title = "A Proof of a Non-Commutative {Central Limit Theorem} by the {Lindeberg} Method", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "5:36--5:50", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1250", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1250", abstract = "A Central Limit Theorem for non-commutative random variables is proved using the Lindeberg method. The theorem is a generalization of the Central Limit Theorem for free random variables proved by Voiculescu. The Central Limit Theorem in this paper relies on an assumption which is weaker than freeness.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "central limit theorem; free convolution; free independence; free probability; Lindeberg method", } @Article{Huang:2007:NIP, author = "Wei Huang and Li-Xin Zhang", title = "A note on the invariance principle of the product of sums of random variables", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "6:51--6:56", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1255", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1255", abstract = "The central limit theorem for the product of sums of various random variables has been studied in a variety of settings. The purpose of this note is to show that this kind of result is a corollary of the invariance principle.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "central limit theorem; invariance of principle; product of sums of r.v.", } @Article{Uemura:2007:EJT, author = "Toshihiro Uemura", title = "On an extension of jump-type symmetric {Dirichlet} forms", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "7:57--7:65", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1256", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1256", abstract = "We show that any element from the ($ L^2$-)maximal domain of a jump-type symmetric Dirichlet form can be approximated by test functions under some conditions. This gives us a direct proof of the fact that the test functions is dense in Bessel potential spaces.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "extended Dirichlet space; jump-type Dirichlet form; Siverstein extension", } @Article{Kuwada:2007:COK, author = "Kazumasa Kuwada and Karl-Theodor Sturm", title = "A counterexample for the optimality of {Kendall--Cranston} coupling", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "8:66--8:72", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1160", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1160", abstract = "We construct a Riemannian manifold where the Kendall--Cranston coupling of two Brownian particle does not maximize the coupling probability.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion; Kendall--Cranston coupling; manifold; optimal coupling", } @Article{Bourgade:2007:EFP, author = "Paul Bourgade and Takahiko Fujita and Marc Yor", title = "{Euler}'s formulae for $ \zeta (2 n) $ and products of {Cauchy} variables", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "9:73--9:80", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1244", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1244", abstract = "We show how to recover Euler's formula for $ \zeta (2 n) $, as well as $ L_{\chi_4}(2 n + 1) $, for any integer $n$, from the knowledge of the density of the product $ \mathbb {C}_1, \mathbb {C}_2 \ldots, \mathbb {C}_k$, for any $ k \geq 1$, where the $ \mathbb {C}_i$'s are independent standard Cauchy variables.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Cauchy variables, stable variables, planar Brownian motion, Euler numbers.", } @Article{Harris:2007:SPB, author = "John Harris and Simon Harris", title = "Survival probabilities for branching {Brownian} motion with absorption", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "10:81--10:92", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1259", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1259", abstract = "We study a branching Brownian motion (BBM) with absorption, in which particles move as Brownian motions with drift $ - \rho $, undergo dyadic branching at rate $ \beta > 0 $, and are killed on hitting the origin. In the case $ \rho > \sqrt {2 \beta } $ the extinction time for this process, $ \zeta $, is known to be finite almost surely. The main result of this article is a large-time asymptotic formula for the survival probability $ P^x(\zeta > t) $ in the case $ \rho > \sqrt {2 \beta } $, where $ P^x $ is the law of the BBM with absorption started from a single particle at the position $ x > 0 $. We also introduce an additive martingale, $V$, for the BBM with absorption, and then ascertain the convergence properties of $V$. Finally, we use $V$ in a `spine' change of measure and interpret this in terms of `conditioning the BBM to survive forever' when $ \rho > \sqrt {2 \beta }$, in the sense that it is the large $t$-limit of the conditional probabilities $ P^x(A \mid \zeta > t + s)$, for $ A \in F_s$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "additive martingales.; Branching Brownian motion with absorption; spine constructions", } @Article{Bose:2007:MCE, author = "Arup Bose and Amites Dasgupta and Krishanu Maulik", title = "Maxima of the cells of an equiprobable multinomial", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "11:93--11:105", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1260", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1260", abstract = "Consider a sequence of multinomial random vectors with increasing number of equiprobable cells. We show that if the number of trials increases fast enough, the sequence of maxima of the cells after a suitable centering and scaling converges to the Gumbel distribution. While results are available for maxima of triangular arrays of independent random variables with certain types of distribution, such results in a dependent setup is new. We also prove that the maxima of a triangular sequence of appropriate Binomial random variables have the same limit distribution. An auxiliary large deviation result for multinomial distribution with increasing number of equiprobable cells may also be of independent interest.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "limit distribution; maxima; Random sequences; triangular array", } @Article{Saintier:2007:GST, author = "Nicolas Saintier", title = "A general stochastic target problem with jump diffusion and an application to a hedging problem for large investors", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "12:106--12:119", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1261", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1261", abstract = "Let $ Z(t, z) $ be a $ \mathbb {R}^d$-valued controlled jump diffusion starting from the point $z$ at time $t$. The aim of this paper is to characterize the set $ V(t)$ of initial conditions $z$ such that $ Z(t, z)$ can be driven into a given target at a given time. We do this by proving that the characteristic function of the complement $ V(t)$ satisfies some partial differential equation in the viscosity sense. As an application, we study the problem of hedging in a financial market with a large investor.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "jump diffusion; large investor; mathematical finance; Stochastic control; viscosity solutions", } @Article{Spitzner:2007:AVF, author = "Dan Spitzner and Thomas Boucher", title = "Asymptotic variance of functionals of discrete-time {Markov} chains via the {Drazin} inverse", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "13:120--13:133", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1262", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1262", abstract = "We consider a $ \psi $-irreducible, discrete-time Markov chain on a general state space with transition kernel $P$. Under suitable conditions on the chain, kernels can be treated as bounded linear operators between spaces of functions or measures and the Drazin inverse of the kernel operator $ I - P$ exists. The Drazin inverse provides a unifying framework for objects governing the chain. This framework is applied to derive a computational technique for the asymptotic variance in the central limit theorems of univariate and higher-order partial sums. Higher-order partial sums are treated as univariate sums on a `sliding-window' chain. Our results are demonstrated on a simple AR(1) model and suggest a potential for computational simplification.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "$f$-regularity; asymptotic variance; Drazin inverse; fundamental matrix; General state space Markov chains; Markov chain central limit theorem", } @Article{DeBlassie:2007:CLL, author = "Dante DeBlassie", title = "The Chance of a Long Lifetime for {Brownian} Motion in a Horn-Shaped Domain", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "14:134--14:139", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1263", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1263", abstract = "By means of a simple conditioning/comparison argument, we derive the chance of a long lifetime for Brownian motion in a horn-shaped domain.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Krikun:2007:CAP, author = "Maxim Krikun", title = "Connected allocation to {Poisson} points in {$ \mathbb {R}^2 $}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "15:140--15:145", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1268", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1268", abstract = "This note answers one question in [1] concerning the connected allocation for the Poisson process in $ \mathbb {R}^2 $. The proposed solution makes use of the Riemann map from the plane minus the minimal spanning forest of the Poisson point process to the halfplane. A picture of a numerically simulated example is included.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Poisson process; Riemann map", } @Article{Patie:2007:TSE, author = "Pierre Patie", title = "Two-sided exit problem for a Spectrally Negative $ \alpha $-Stable {Ornstein--Uhlenbeck} Process and the {Wright}'s generalized hypergeometric functions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "16:146--16:160", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1265", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1265", abstract = "The Laplace transform of the first exit time from a finite interval by a regular spectrally negative $ \alpha $-stable Ornstein--Uhlenbeck process is provided in terms of the Wright's generalized hypergeometric function. The Laplace transform of first passage times is also derived for some related processes such as the process killed when it enters the negative half line and the process conditioned to stay positive. The law of the maximum of the associated bridges is computed in terms of the $q$-resolvent density. As a byproduct, we deduce some interesting analytical properties for some Wright's generalized hypergeometric functions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "stable Ornstein--Uhlenbeck process; Two-sided exit time; Wright's generalized hypergeometric functions", } @Article{Bojdecki:2007:SEF, author = "Tomasz Bojdecki and Luis Gorostiza and Anna Talarczyk", title = "Some Extensions of Fractional {Brownian} Motion and Sub-Fractional {Brownian} Motion Related to Particle Systems", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "17:161--17:172", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1272", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1272", abstract = "In this paper we study three self-similar, long-range dependence, Gaussian processes. The first one, with covariance\par $$ \int^{s \wedge t}_0 u^a [(t - u)^b + (s - u)^b]d u, $$ parameters $ a > - 1 $, $ - 1 < b \leq 1 $, $ |b| \leq 1 + a $, corresponds to fractional Brownian motion for $ a = 0 $, $ - 1 < b < 1 $. The second one, with covariance\par $$ (2 - h) \biggl (s^h + t^h - \frac {1}{2}[(s + t)^h + |s - t|^h] \biggr), $$ parameter $ 0 < h \leq 4 $, corresponds to sub-fractional Brownian motion for $ 0 < h < 2 $. The third one, with covariance\par $$ - \left (s^2 \log s + t^2 \log t - \frac {1}{2}[(s + t)^2 \log (s + t) + (s - t)^2 \log |s - t|] \right), $$ is related to the second one. These processes come from occupation time fluctuations of certain particle systems for some values of the parameters.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "bi-fractional Brownian motion; fractional Brownian motion; long-range dependence; negative sub-fractional Brownian motion; particle system; sub-fractional Brownian motion; weighted fractional Brownian motion", } @Article{Funaki:2007:DSL, author = "Tadahisa Funaki", title = "Dichotomy in a scaling limit under {Wiener} measure with density", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "18:173--18:183", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1271", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1271", abstract = "In general, if the large deviation principle holds for a sequence of probability measures and its rate functional admits a unique minimizer, then the measures asymptotically concentrate in its neighborhood so that the law of large numbers follows. This paper discusses the situation that the rate functional has two distinct minimizers, for a simple model described by the pinned Wiener measures with certain densities involving a scaling. We study their asymptotic behavior and determine to which minimizers they converge based on a more precise investigation than the large deviation's level.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Large deviation principle, minimizers, pinned Wiener measure, scaling limit, concentration", } @Article{Bercu:2007:ARE, author = "Bernard Bercu and W{\l}odek Bryc", title = "Asymptotic results for empirical measures of weighted sums of independent random variables", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "19:184--19:199", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1273", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1273", abstract = "We investigate the asymptotic behavior of weighted sums of independent standardized random variables with uniformly bounded third moments. The sequence of weights is given by a family of rectangular matrices with uniformly small entries and approximately orthogonal rows. We prove that the empirical CDF of the resulting partial sums converges to the normal CDF with probability one. This result implies almost sure convergence of empirical periodograms, almost sure convergence of spectral distribution of circulant and reverse circulant matrices, and almost sure convergence of the CDF generated from independent random variables by independent random orthogonal matrices. In the special case of trigonometric weights, the speed of the almost sure convergence is described by a normal approximation as well as a large deviation principle.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Bose:2007:APR, author = "Arup Bose and Arnab Sen", title = "On asymptotic properties of the rank of a special random adjacency matrix", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "20:200--20:205", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1266", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1266", abstract = "Consider the matrix $ \Delta_n = ((\ \mathrm {I}(X_i + X_j > 0))_{i, j = 1, 2, \ldots {}, n} $ where $ \{ X_i \} $ are i.i.d.\ and their distribution is continuous and symmetric around $0$. We show that the rank $ r_n$ of this matrix is equal in distribution to $ 2 \sum_{i = 1}^{n - 1} \mathrm {I}(\xi_i = 1, \xi_{i + 1} = 0) + \mathrm {I}(\xi_n = 1)$ where $ \xi_i \stackrel {i.i.d.}{\sim } \text {Ber} (1, 1 / 2).$ As a consequence $ \sqrt n(r_n / n - 1 / 2)$ is asymptotically normal with mean zero and variance $ 1 / 4$. We also show that $ n^{-1}r_n$ converges to $ 1 / 2$ almost surely.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Large dimensional random matrix, rank, almost sure representation, $1$-dependent sequence, almost sure convergence, convergence in distribution.", } @Article{Hutzenthaler:2007:GRS, author = "Martin Hutzenthaler and Roland Alkemper", title = "Graphical representation of some duality relations in stochastic population models", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "21:206--21:220", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1283", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1283", abstract = "We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. MR2123250) and for the self-duality of Feller's branching diffusion with logistic growth (cf. MR2308333). The two dual processes are approximated by particle processes which are forward and backward processes in a graphical representation. We identify duality relations between the basic building blocks of the particle processes which lead to the two dualities mentioned above.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "branching-coalescing particle process; Duality; Feller's branching diffusion; graphical representation; resampling-selection model; stochastic population dynamics", } @Article{Liu:2007:SLT, author = "Wei-Dong Liu and Zheng-Yan Lin", title = "Some {LIL} type results on the partial sums and trimmed sums with multidimensional indices", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "22:221--22:233", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1286", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1286", abstract = "Let $ \{ X, X_{{n}}; n \in \mathbb {N}^d \} $ be a field of i.i.d. random variables indexed by $d$-tuples of positive integers and let $ S_{{n}} = \sum_{{k} \leq {n}}X_{{k}}$. We prove some strong limit theorems for $ S_{{n}}$. Also, when $ d \geq 2$ and $ h({n})$ satisfies some conditions, we show that there are no LIL type results for $ S_{{n}} / \sqrt {|{n}|h({n})}$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Law of the iterated logarithm; random field; trimmed sums", } @Article{Spruill:2007:ADC, author = "Marcus Spruill", title = "Asymptotic Distribution of Coordinates on High Dimensional Spheres", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "23:234--23:247", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1294", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1294", abstract = "The coordinates $ x_i $ of a point $ x = (x_1, x_2, \dots, x_n) $ chosen at random according to a uniform distribution on the $ \ell_2 (n)$-sphere of radius $ n^{1 / 2}$ have approximately a normal distribution when $n$ is large. The coordinates $ x_i$ of points uniformly distributed on the $ \ell_1 (n)$-sphere of radius $n$ have approximately a double exponential distribution. In these and all the $ \ell_p(n), 1 \le p \le \infty, $ convergence of the distribution of coordinates as the dimension $n$ increases is at the rate $ \sqrt {n}$ and is described precisely in terms of weak convergence of a normalized empirical process to a limiting Gaussian process, the sum of a Brownian bridge and a simple normal process.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "dependent arrays; empiric distribution; isoperimetry; micro-canonical ensemble; Minkowski area", } @Article{Rao:2007:MFR, author = "N. Raj Rao and Roland Speicher", title = "Multiplication of free random variables and the {$S$}-transform: the case of vanishing mean", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "24:248--24:258", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1274", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1274", abstract = "This note extends Voiculescu's {\em S\/}-transform based analytical machinery for free multiplicative convolution to the case where the mean of the probability measures vanishes. We show that with the right interpretation of the {\em S\/}-transform in the case of vanishing mean, the usual formula makes perfectly good sense.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "free multiplicative convolution; Random matrices, free probability", } @Article{Jost:2007:NET, author = "C{\'e}line Jost", title = "A note on ergodic transformations of self-similar {Volterra} {Gaussian} processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "25:259--25:266", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1298", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1298", abstract = "We derive a class of ergodic transformation of self-similar Gaussian processes that are Volterra, i.e. of type $ X_t = \int^t_0 z_X(t, s)d W_s $, $ t \in [0, \infty) $, where $ z_X $ is a deterministic kernel and $W$ is a standard Brownian motion.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Ergodic transformation; Fractional Brownian motion; Self-similar process; Volterra Gaussian process", } @Article{Yang:2007:TMP, author = "Ming Yang", title = "On a theorem in multi-parameter potential theory", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "26:267--26:275", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1293", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1293", abstract = "We prove that the expected Lebesgue measure of the range of an additive L{\'e}vy process is positive if and only if the product $ \Re ([1 + \Psi_1 (\xi)]^{-1}) \ldots {} \Re ([1 + \Psi_N(\xi)]^{-1}) $ is integrable. This was previously proved by Khoshnevisan, Xiao and Zhong [1] under a sector condition.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Additive L{\'e}vy processes, Hausdorff dimension, multiple points.", } @Article{Tamas:2007:DDN, author = "M{\'o}ri Tam{\'a}s", title = "Degree distribution nearby the origin of a preferential attachment graph", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "27:276--27:282", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1299", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1299", abstract = "In a 2-parameter scale free model of random graphs it is shown that the asymptotic degree distribution is the same in the neighbourhood of every vertex. This degree distribution is still a power law with characteristic exponent 2, but this exponent is different from the one observed in the whole graph.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "degree distribution; martingale; Scale free graphs", } @Article{Arguin:2007:DCP, author = "Louis-Pierre Arguin", title = "A dynamical characterization of {Poisson--Dirichlet} distributions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "28:283--28:290", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1300", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1300", abstract = "We show that a slight modification of a theorem of Ruzmaikina and Aizenman on competing particle systems on the real line leads to a characterization of Poisson--Dirichlet distributions $ P D(\alpha, 0) $. Precisely, let $ \xi $ be a proper random mass-partition i.e. a random sequence $ (\xi_i, i \in N) $ such that $ \xi_1 \geq \xi_2 \geq \dots \geq 0 $ and $ \sum_i \xi_i = 1 $ a.s. Consider $ \{ W_i \}_{i \in N} $, an iid sequence of random positive numbers whose distribution is absolutely continuous with respect to the Lebesgue measure and $ E[W^\lambda] < \infty $ for all $ \lambda \in R $. It is shown that, if the law of $ \xi $ is invariant under the random reshuffling\par $$ (\xi_i, i \in N) \to \left (\frac {\xi_i W_i}{\sum_j \xi_jW_j }, i \in N \right) $$ where the weights are reordered after evolution, then it must be a mixture of Poisson--Dirichlet distributions $ P D(\alpha, 0), \alpha \in (0, 1) $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Point processes, Poisson--Dirichlet distributions", } @Article{Baldi:2007:CIG, author = "Paolo Baldi and Domenico Marinucci and Veeravalli Varadarajan", title = "On the characterization of isotropic {Gaussian} fields on homogeneous spaces of compact groups", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "29:291--29:302", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1316", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1316", abstract = "Let $T$ be a random field weakly invariant under the action of a compact group $G$. We give conditions ensuring that independence of the random Fourier coefficients is equivalent to Gaussianity. As a consequence, in general it is not possible to simulate a non-Gaussian invariant random field through its Fourier expansion using independent coefficients", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "isotropic Random Fields, Fourier expansions, Characterization of Gaussian Random Fields", } @Article{Berard:2007:CLT, author = "Jean Berard and Alejandro Ramirez", title = "{Central Limit Theorem} For The Excited Random Walk In Dimension $ d \geq 2 $", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "30:303--30:314", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1317", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1317", abstract = "We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension $ d \geq 2 $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Excited random walk, Regeneration techniques", } @Article{Meckes:2007:SNR, author = "Mark Meckes", title = "On the spectral norm of a random {Toeplitz} matrix", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "31:315--31:325", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1313", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1313", abstract = "Suppose that $ T_n $ is a Toeplitz matrix whose entries come from a sequence of independent but not necessarily identically distributed random variables with mean zero. Under some additional tail conditions, we show that the spectral norm of $ T_n $ is of the order $ \sqrt {n \log n} $. The same result holds for random Hankel matrices as well as other variants of random Toeplitz matrices which have been studied in the literature.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "random Toeplitz matrix, random Hankel matrix, spectral norm", } @Article{Zerner:2007:ZOL, author = "Martin Zerner", title = "The zero-one law for planar random walks in i.i.d. random environments revisited", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "32:326--32:335", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1314", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1314", abstract = "In this note we present a simplified proof of the zero-one law by Merkl and Zerner (2001) for directional transience of random walks in i.i.d. random environments (RWRE) on the square lattice. Also, we indicate how to construct a two-dimensional counterexample in a non-uniformly elliptic and stationary environment which has better ergodic properties than the example given by Merkl and Zerner.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random environment, random walk, RWRE, transience, zero-one law", } @Article{Andrieu:2007:EAM, author = "Christophe Andrieu and Yves Atchade", title = "On the efficiency of adaptive {MCMC} algorithms", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "33:336--33:349", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1320", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1320", abstract = "We study a class of adaptive Markov Chain Monte Carlo (MCMC) processes which aim at behaving as an ``optimal'' target process via a learning procedure. We show, under appropriate conditions, that the adaptive MCMC chain and the ``optimal'' (nonadaptive) MCMC process share many asymptotic properties. The special case of adaptive MCMC algorithms governed by stochastic approximation is considered in details and we apply our results to the adaptive Metropolis algorithm of [Haario, Saksman, Tamminen].", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Peccati:2007:GAM, author = "Giovanni Peccati", title = "{Gaussian} Approximations of Multiple Integrals", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "34:350--34:364", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1322", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1322", abstract = "Fix $ k \geq 1 $, and let $ I(l), l \geq 1 $, be a sequence of $k$-dimensional vectors of multiple Wiener-It{\^o} integrals with respect to a general Gaussian process. We establish necessary and sufficient conditions to have that, as $ l \to \infty $, the law of $ I(l)$ is asymptotically close (for example, in the sense of Prokhorov's distance) to the law of a $k$-dimensional Gaussian vector having the same covariance matrix as $ I(l)$. The main feature of our results is that they require minimal assumptions (basically, boundedness of variances) on the asymptotic behaviour of the variances and covariances of the elements of $ I(l)$. In particular, we will not assume that the covariance matrix of $ I(l)$ is convergent. This generalizes the results proved in Nualart and Peccati (2005), Peccati and Tudor (2005) and Nualart and Ortiz-Latorre (2007). As shown in Marinucci and Peccati (2007b), the criteria established in this paper are crucial in the study of the high-frequency behaviour of stationary fields defined on homogeneous spaces.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Gaussian processes; Malliavin calculus; Multiple stochastic integrals; Non-central limit theorems; Weak convergence", } @Article{Benjamini:2007:MAP, author = "Itai Benjamini and Ariel Yadin and Ofer Zeitouni", title = "Maximal Arithmetic Progressions in Random Subsets", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "35:365--35:376", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1321", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", note = "See erratum \cite{Benjamini:2012:EMA}.", URL = "http://ecp.ejpecp.org/article/view/1321", abstract = "Let $ U(N) $ denote the maximal length of arithmetic progressions in a random uniform subset of $ \{ 0, 1 \}^N $. By an application of the Chen-Stein method, we show that $ U(N) - 2 \log (N) / \log (2) $ converges in law to an extreme type (asymmetric) distribution. The same result holds for the maximal length $ W(N) $ of arithmetic progressions (mod $N$). When considered in the natural way on a common probability space, we observe that $ U(N) / \log (N)$ converges almost surely to $ 2 / \log (2)$, while $ W(N) / \log (N)$ does not converge almost surely (and in particular, $ \limsup W(N) / \log (N)$ is at least $ 3 / \log (2)$).\par \url{https://doi.org/10.1214/ECP.v17-2014} {\bf An Erratum is available in ECP volume {\bf 17} paper number 18.}", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "arithmetic progression; Chen-Stein method; dependency graph; extreme type limit distribution; random subset", } @Article{Montenegro:2007:SEV, author = "Ravi Montenegro", title = "Sharp edge, vertex, and mixed {Cheeger} type inequalities for finite {Markov} kernels", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "36:377--36:389", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1269", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1269", abstract = "We show how the evolving set methodology of Morris and Peres can be used to show Cheeger inequalities for bounding the spectral gap of a finite Markov kernel. This leads to sharp versions of several previous Cheeger inequalities, including ones involving edge-expansion, vertex-expansion, and mixtures of both. A bound on the smallest eigenvalue also follows.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Markov chain, evolving sets, Cheeger inequality, eigenvalues", } @Article{Darses:2007:DPC, author = "S{\'e}bastien Darses and Ivan Nourdin", title = "Dynamical properties and characterization of gradient drift diffusions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "37:390--37:400", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1324", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1324", abstract = "We study the dynamical properties of the Brownian diffusions having $ \sigma \, {\rm Id} $ as diffusion coefficient matrix and $ b = \nabla U $ as drift vector. We characterize this class through the equality $ D^2_+= D^2_- $, where $ D_+ $ (resp. $ D_-$) denotes the forward (resp. backward) stochastic derivative of Nelson's type. Our proof is based on a remarkable identity for $ D_+^2 - D_-^2$ and on the use of the martingale problem.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Gradient drift diffusion; Kolmogorov theorem; Martingale problem; Nelson stochastic derivatives; Reversible diffusion; Stationary diffusion; Time reversal", } @Article{Panchenko:2007:NTP, author = "Dmitriy Panchenko", title = "A note on {Talagrand}'s positivity principle", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "38:401--38:410", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1326", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1326", abstract = "Talagrand's positivity principle states that one can slightly perturb a Hamiltonian in the Sherrington-Kirkpatrick model in such a way that the overlap of two configurations under the perturbed Gibbs' measure will become typically nonnegative. In this note we observe that abstracting from the setting of the SK model only improves the result and does not require any modifications in Talagrand's argument. In this version, for example, positivity principle immediately applies to the setting of replica symmetry breaking interpolation. Also, abstracting from the SK model improves the conditions in the Ghirlanda-Guerra identities and as a consequence results in a perturbation of smaller order necessary to ensure positivity of the overlap.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Talagrand's positivity principle, Ghirlanda-Guerra identities", } @Article{vandenBerg:2007:SPI, author = "Jacob van den Berg and Antal Jarai and Balint Vagvolgyi", title = "The size of a pond in 2D invasion percolation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "39:411--39:420", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1327", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1327", abstract = "We consider invasion percolation on the square lattice. van den Berg, Peres, Sidoravicius and Vares have proved that the probability that the radius of a so-called pond is larger than n, differs at most a factor of order log n from the probability that in critical Bernoulli percolation the radius of an open cluster is larger than n. We show that these two probabilities are, in fact, of the same order. Moreover, we prove an analogous result for the volume of a pond.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "critical percolation; invasion percolation; pond", } @Article{Cox:2007:SRT, author = "Sonja Cox and Mark Veraar", title = "Some remarks on tangent martingale difference sequences in {$ L^1 $}-spaces", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "40:421--40:433", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1328", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1328", abstract = "Let $X$ be a Banach space. Suppose that for all $ p \in (1, \infty)$ a constant $ C_{p, X}$ depending only on $X$ and $p$ exists such that for any two $X$-valued martingales $f$ and $g$ with tangent martingale difference sequences one has\par $$ \mathbb {E} \| f \|^p \leq C_{p, X} \mathbb {E} \| g \|^p \qquad (*). $$ This property is equivalent to the UMD condition. In fact, it is still equivalent to the UMD condition if in addition one demands that either $f$ or $g$ satisfy the so-called (CI) condition. However, for some applications it suffices to assume that $ (*)$ holds whenever $g$ satisfies the (CI) condition. We show that the class of Banach spaces for which $ (*)$ holds whenever only $g$ satisfies the (CI) condition is more general than the class of UMD spaces, in particular it includes the space $ L^1$. We state several problems related to $ (*)$ and other decoupling inequalities.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Davis decomposition; decoupling inequalities; martingale difference sequences; tangent sequences; UMD Banach spaces", } @Article{Van:2007:SLL, author = "Thanh Le Van", title = "On the strong law of large numbers for $d$-dimensional arrays of random variables", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "41:434--41:441", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1331", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1331", abstract = "In this paper, we provide a necessary and sufficient condition for general $d$-dimensional arrays of random variables to satisfy strong law of large numbers. Then, we apply the result to obtain some strong laws of large numbers for $d$-dimensional arrays of blockwise independent and blockwise orthogonal random variables.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Strong law of large number, almost sure convergence, $d$-dimensional arrays of random variables", } @Article{DaPrato:2007:MKP, author = "Giuseppe {Da Prato} and Arnaud Debussche and Luciano Tubaro", title = "A modified {Kardar--Parisi--Zhang} model", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "42:442--42:453", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1333", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1333", abstract = "A one dimensional stochastic differential equation of the form $$ d X = A X d t + \frac 12 ( - A)^{- \alpha } \partial_\xi [(( - A)^{- \alpha }X)^2]d t + \partial_\xi d W(t), \qquad X(0) = x $$ is considered, where $ A = \frac 12 \partial^2_\xi $. The equation is equipped with periodic boundary conditions. When $ \alpha = 0 $ this equation arises in the Kardar--Parisi--Zhang model. For $ \alpha \ne 0 $, this equation conserves two important properties of the Kardar--Parisi--Zhang model: it contains a quadratic nonlinear term and has an explicit invariant measure which is Gaussian. However, it is not as singular and using renormalization and a fixed point result we prove existence and uniqueness of a strong solution provided $ \alpha > \frac 18 $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "invariant measure; Stochastic partial differential equations; white noise; Wick product", } @Article{Haggstrom:2007:VCM, author = "Olle H{\"a}ggstr{\"om} and Jeffrey Rosenthal", title = "On Variance Conditions for {Markov} Chain {CLTs}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "43:454--43:464", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1336", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1336", abstract = "Central limit theorems for Markov chains are considered, and in particular the relationships between various expressions for asymptotic variance known from the literature. These turn out to be equal under fairly general conditions, although not always. We also investigate the existence of CLTs, and pose some open problems.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Oraby:2007:SLH, author = "Tamer Oraby", title = "The spectral laws of {Hermitian} block-matrices with large random blocks", journal = j-ELECTRON-COMMUN-PROBAB, volume = "12", pages = "44:465--44:476", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v12-1335", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1335", abstract = "We are going to study the limiting spectral measure of fixed dimensional Hermitian block-matrices with large dimensional Wigner blocks. We are going also to identify the limiting spectral measure when the Hermitian block-structure is Circulant. Using the limiting spectral measure of a Hermitian Circulant block-matrix we will show that the spectral measure of a Wigner matrix with k-weakly dependent entries need not to be the semicircle law in the limit.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random matrices", } @Article{Fierro:2007:SSA, author = "Raul Fierro and Soledad Torres", title = "A stochastic scheme of approximation for ordinary differential equations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "1:1--1:9", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1341", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1341", abstract = "In this note we provide a stochastic method for approximating solutions of ordinary differential equations. To this end, a stochastic variant of the Euler scheme is given by means of Markov chains. For an ordinary differential equation, these approximations are shown to satisfy a Large Number Law, and a Central Limit Theorem for the corresponding fluctuations about the solution of the differential equation is proven.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Central limit theorem; Convergence in law; Numerical Scheme", } @Article{Feyel:2007:NCS, author = "Denis Feyel and Arnaud {de La Pradelle} and Gabriel Mokobodzki", title = "A non-commutative sewing lemma", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "3:24--3:34", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1345", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1345", abstract = "A non-commutative version of the sewing lemma is proved, with some applications", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Curvilinear Integrals, Rough Paths, Stochastic Integrals", } @Article{Wu:2008:LDP, author = "Liming Wu and Nian Yao", title = "Large deviation principles for {Markov} processes via {Phi--Sobolev} inequalities", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "2:10--2:23", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1342", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1342", abstract = "Via Phi-Sobolev inequalities, we give some sharp integrability conditions on $F$ for the large deviation principle of the empirical mean $ \frac {1}{T}{\int_0^T{F(X_s)}ds}$ for large time $T$, where $F$ is unbounded with values in some separable Banach space. Several examples are provided.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "functional inequalities; large deviations; Orlicz space", } @Article{Rossignol:2008:TPP, author = "Rapha{\"e}l Rossignol", title = "Threshold phenomena on product spaces: BKKKL revisited (once more)", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "4:35--4:44", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1344", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1344", abstract = "We revisit the work of Bourgain et al. (1992) - referred to as {"BKKKL"} in the title - about influences on Boolean functions in order to give a precise statement of threshold phenomenon on the product space $ \{ 1, \ldots {}, r \}^N $, generalizing one of the main results of Talagrand (1994).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Threshold phenomenon, approximate zero-one law, influences.", } @Article{LePrince:2008:RBD, author = "Vincent {Le Prince}", title = "A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "5:45--5:53", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1350", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1350", abstract = "We establish in this paper an exact formula which links the dimension of the harmonic measure, the asymptotic entropy and the rate of escape for a random walk on a discrete subgroup of the isometry group of a Gromov hyperbolic space. This completes a result obtained by the author in a previous paper, where only an upper bound for the dimension was proved.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "drift; entropy; harmonic measure; hyperbolic space; Random walk", } @Article{vanZanten:2008:REG, author = "Harry van Zanten", title = "A remark on the equivalence of {Gaussian} processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "6:54--6:59", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1348", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1348", abstract = "In this note we extend a classical equivalence result for Gaussian stationary processes to the more general setting of Gaussian processes with stationary increments. This will allow us to apply it in the setting of aggregated independent fractional Brownian motions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "equivalence of laws, spectral method; Gaussian processes with stationary increments", } @Article{Bakry:2008:SPP, author = "Dominique Bakry and Franck Barthe and Patrick Cattiaux and Arnaud Guillin", title = "A simple proof of the {Poincar{\'e}} inequality for a large class of probability measures", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "7:60--7:66", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1352", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1352", abstract = "Abstract. We give a simple and direct proof of the existence of a spectral gap under some Lyapunov type condition which is satisfied in particular by log-concave probability measures on $ \mathbb {R}^n $. The proof is based on arguments introduced in Bakry and al, but for the sake of completeness, all details are provided.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Lyapunov functions, Poincar{\'e} inequality, log-concave measure", } @Article{Lawi:2008:HLP, author = "Stephan Lawi", title = "{Hermite} and {Laguerre} Polynomials and Matrix-Valued Stochastic Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "8:67--8:84", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1353", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1353", abstract = "We extend to matrix-valued stochastic processes, some well-known relations between real-valued diffusions and classical orthogonal polynomials, along with some recent results about L{\'e}vy processes and martingale polynomials. In particular, joint semigroup densities of the eigenvalue processes of the generalized matrix-valued Ornstein--Uhlenbeck and squared Ornstein--Uhlenbeck processes are respectively expressed by means of the Hermite and Laguerre polynomials of matrix arguments. These polynomials also define martingales for the Brownian matrix and the generalized Gamma process. As an application, we derive a chaotic representation property for the eigenvalue process of the Brownian matrix.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian matrices, Wishart processes, Hermite polynomials, Laguerre polynomials, martingale polynomials, chaos representation property", } @Article{Bednorz:2008:RPC, author = "Witold Bednorz and Krzysztof Latuszynski and Rafal Latala", title = "A Regeneration Proof of the {Central Limit Theorem} for Uniformly Ergodic {Markov} Chains", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "9:85--9:98", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1354", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1354", abstract = "Central limit theorems for functionals of general state space Markov chains are of crucial importance in sensible implementation of Markov chain Monte Carlo algorithms as well as of vital theoretical interest. Different approaches to proving this type of results under diverse assumptions led to a large variety of CLT versions. However due to the recent development of the regeneration theory of Markov chains, many classical CLTs can be reproved using this intuitive probabilistic approach, avoiding technicalities of original proofs. In this paper we provide a characterization of CLTs for ergodic Markov chains via regeneration and then use the result to solve the open problem posed in [Roberts \& Rosenthal 2005]. We then discuss the difference between one-step and multiple-step small set condition.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Markov chains, central limit theorems, regeneration, ergodicity, uniform ergodicity, Harris recurrence", } @Article{McVinish:2008:OPE, author = "Ross McVinish", title = "Optimising prediction error among completely monotone covariance sequences", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "11:113--11:120", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1355", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1355", abstract = "We provide a characterisation of Gaussian time series which optimise the one-step prediction error subject to the covariance sequence being completely monotone with the first {\em m\/} covariances specified.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "aggregation; maximum entropy; moment space", } @Article{Gao:2008:EEM, author = "Fuchang Gao", title = "Entropy Estimate for $k$-Monotone Functions via Small Ball Probability of Integrated {Brownian} Motions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "12:121--12:130", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1357", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1357", abstract = "Metric entropy of the class of probability distribution functions on $ [0, 1] $ with a $k$-monotone density is studied through its connection with the small ball probability of $k$-times integrated Brownian motions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "metric entropy, $k$-monotone function, small ball probability, $k$-times integrated Brownian motion", } @Article{Rolla:2008:LPP, author = "Leonardo Rolla and Augusto Teixeira", title = "Last Passage Percolation in Macroscopically Inhomogeneous Media", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "13:131--13:139", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1287", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1287", abstract = "In this note we investigate the last passage percolation model in the presence of macroscopic inhomogeneity. We analyze how this affects the scaling limit of the passage time, leading to a variational problem that provides an ODE for the deterministic limiting shape of the maximal path. We obtain a sufficient analytical condition for uniqueness of the solution for the variational problem. Consequences for the totally asymmetric simple exclusion process are discussed.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "inhomogeneous media; last passage percolation; scaling limit; tasep; variational problem", } @Article{Windisch:2008:RWD, author = "David Windisch", title = "Random walk on a discrete torus and random interlacements", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "14:140--14:150", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1359", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1359", abstract = "We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus $ ({\mathbb Z} / N{\mathbb Z})^d $, $ d \geq 3 $, until $ u N^d $ time steps, $ u > 0 $, and the model of random interlacements recently introduced by Sznitman. In particular, we show that for large $N$, the joint distribution of the local pictures in the neighborhoods of finitely many distant points left by the walk up to time $ u N^d$ converges to independent copies of the random interlacement at level $u$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "random interlacements; Random walk", } @Article{Maas:2008:COF, author = "Jan Maas and Jan Neerven", title = "A {Clark--Ocone} formula in {UMD} {Banach} spaces", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "15:151--15:164", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1361", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1361", abstract = "Let $H$ be a separable real Hilbert space and let $ \mathbb {F} = (\mathscr {F}_t)_{t \in [0, T]}$ be the augmented filtration generated by an $H$-cylindrical Brownian motion $ (W_H(t))_{t \in [0, T]}$ on a probability space $ (\Omega, \mathscr {F}, \mathbb {P})$. We prove that if $E$ is a UMD Banach space, $ 1 \le p < \infty $, and $ F \in \mathbb {D}^{1, p}(\Omega; E)$ is $ \mathscr {F}_T$-measurable, then\par $$ F = \mathbb {E} (F) + \int_0^T P_{\mathbb {F}} (D F) \, d W_H, $$ where $D$ is the Malliavin derivative of $F$ and $ P_{\mathbb {F}}$ is the projection onto the $ {\mathbb {F}}$-adapted elements in a suitable Banach space of $ L^p$-stochastically integrable $ \mathscr {L}(H, E)$-valued processes.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Clark-Ocone formula, Malliavin calculus", } @Article{Sturm:2008:TVM, author = "Anja Sturm and Jan Swart", title = "Tightness of voter model interfaces", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "16:165--16:174", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1360", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1360", abstract = "Consider a long-range, one-dimensional voter model started with all zeroes on the negative integers and all ones on the positive integers. If the process obtained by identifying states that are translations of each other is positively recurrent, then it is said that the voter model exhibits interface tightness. In 1995, Cox and Durrett proved that one-dimensional voter models exhibit interface tightness if their infection rates have a finite third moment. Recently, Belhaouari, Mountford, and Valle have improved this by showing that a finite second moment suffices. The present paper gives a new short proof of this fact. We also prove interface tightness for a long range swapping voter model, which has a mixture of long range voter model and exclusion process dynamics.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "exclusion process.; interface tightness; Long range voter model; swapping voter model", } @Article{Latala:2008:BBP, author = "Rafal Latala", title = "On the boundedness of {Bernoulli} processes over thin sets", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "17:175--17:186", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1362", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1362", abstract = "We show that the Bernoulli conjecture holds for sets with small one-dimensional projections, i.e. any bounded Bernoulli process indexed by such set may be represented as a sum of a uniformly bounded process and a process dominated by a bounded Gaussian process.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Bernoulli process, Bernoulli conjecture, partitioning scheme, majorizing measure", } @Article{Gnedin:2008:CRP, author = "Alexander Gnedin", title = "Corners and Records of the {Poisson} Process in Quadrant", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "18:187--18:193", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1351", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1351", abstract = "The scale-invariant spacings lemma due to Arratia, Barbour and Tavar{\'e} establishes the distributional identity of a self-similar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of a certain set of extreme points of the unit Poisson process in the positive quadrant", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "$k$-records, $k$-corners, self-similar Poisson process, Ignatov's theorem", } @Article{Pal:2008:SB, author = "Soumik Pal", title = "Symmetrization of {Bernoulli}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "19:194--19:197", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1364", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1364", abstract = "We show that an asymmetric Bernoulli random variable is symmetry resistant in the sense that any independent random variable, which when added to it produces a symmetric sum, must have a variance at least as much as itself. The main instrument is to use Skorokhod embedding to transfer the discrete problem to the realm of stochastic calculus.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Symmetrization, symmetry resistant, Skorokhod embedding", } @Article{Eisenbaum:2008:PGG, author = "Nathalie Eisenbaum and Andreas Kyprianou", title = "On the parabolic generator of a general one-dimensional {L{\'e}vy} process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "20:198--20:209", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1366", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1366", abstract = "The purpose of this note is twofold. Firstly to complete a recent accumulation of results concerning extended version of Ito's formula for any one dimensional L{\'e}vy processes, $X$. Secondly, we use the latter to characterise the parabolic generator of $X$, $$ {\bf A} := \left \{ (f, g) : f(X_\cdot, \cdot) - \int_0^\cdot g(X_s, s)d s \text { is a local martingale} \right \} . $$ We also establish a necessary condition for a pair of functions to be in the domain of the parabolic generator when $X$ has a Gaussian component.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stochastic calculus , local time-space, It{\^o} formula, parabolic generator.", } @Article{Makhnin:2008:FPE, author = "Oleg Makhnin", title = "Filtering and parameter estimation for a jump stochastic process with discrete observations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "21:210--21:224", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1363", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1363", abstract = "A compound Poisson process is considered. We estimate the current position of the stochastic process based on past discrete-time observations (non-linear discrete filtering problem) in Bayesian setting. We obtain bounds for the asymptotic rate of the expected square error of the filter when observations become frequent. The bounds depend linearly on jump intensity. Also, estimation of process' parameters is addressed.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Comman:2008:SWT, author = "Henri Comman", title = "{Stone--Weierstrass} type theorems for large deviations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "22:225--22:240", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1370", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1370", abstract = "We give a general version of Bryc's theorem valid on any topological space and with any algebra $ \mathcal {A} $ of real-valued continuous functions separating the points, or any well-separating class. In absence of exponential tightness, and when the underlying space is locally compact regular and $ \mathcal {A} $ constituted by functions vanishing at infinity, we give a sufficient condition on the functional $ \Lambda (\cdot)_{\mid \mathcal {A}} $ to get large deviations with not necessarily tight rate function. We obtain the general variational form of any rate function on a completely regular space; when either exponential tightness holds or the space is locally compact Hausdorff, we get it in terms of any algebra as above. Prohorov-type theorems are generalized to any space, and when it is locally compact regular the exponential tightness can be replaced by a (strictly weaker) condition on $ \Lambda (\cdot)_{\mid \mathcal {A}} $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Large deviations, rate function, Bryc's theorem", } @Article{Panchenko:2008:DPF, author = "Dmitry Panchenko", title = "On differentiability of the {Parisi} formula", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "23:241--23:247", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1365", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1365", abstract = "It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using approximate solutions in the Parisi formula and give one example of application of the differentiability to prove non self-averaging of the overlap outside of the replica symmetric region.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Sherrington-Kirkpatrick model, Parisi formula.", } @Article{Miermont:2008:SSL, author = "Gr{\'e}gory Miermont", title = "On the sphericity of scaling limits of random planar quadrangulations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "24:248--24:257", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1368", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1368", abstract = "We give a new proof of a theorem by Le Gall and Paulin, showing that scaling limits of random planar quadrangulations are homeomorphic to the 2-sphere. The main geometric tool is a reinforcement of the notion of Gromov-Hausdorff convergence, called 1-regular convergence, that preserves topological properties of metric surfaces.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random planar maps, scaling limits, Gromov-Hausdorff convergence, spherical topology", } @Article{Wastlund:2008:RMP, author = "Johan W{\"a}stlund", title = "Random matching problems on the complete graph", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "25:258--25:265", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1372", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1372", abstract = "The edges of the complete graph on $n$ vertices are assigned independent exponentially distributed costs. A $k$-matching is a set of $k$ edges of which no two have a vertex in common. We obtain explicit bounds on the expected value of the minimum total cost $ C_{k, n}$ of a $k$-matching. In particular we prove that if $ n = 2 k$ then $ \pi^2 / 12 < E C_{k, n} < \pi^2 / 12 + \log n / n$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Minimum matching, exponential, expectation, mean field, network.", } @Article{Bobkov:2008:NDM, author = "Sergey Bobkov", title = "A note on the distributions of the maximum of linear {Bernoulli} processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "26:266--26:271", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1375", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1375", abstract = "We give a characterization of the family of all probability measures on the extended line $ ( - \infty, + \infty] $, which may be obtained as the distribution of the maximum of some linear Bernoulli process.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "distribution of the maximum; Linear Bernoulli processes", } @Article{Huss:2008:IDL, author = "Wilfried Huss", title = "Internal Diffusion-Limited Aggregation on non-amenable graphs", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "27:272--27:279", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1374", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1374", abstract = "The stochastic growth model Internal Diffusion Limited Aggregation was defined in 1991 by Diaconis and Fulton. Several shape results are known when the underlying state space is the d-dimensional lattice, or a discrete group with exponential growth. We prove an extension of the shape result of Blachere and Brofferio for Internal Diffusion Limited Aggregation on a wide class of Markov chains on non-amenable graphs.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "interacting particle systems; random walks on graphs", } @Article{Peche:2008:LBS, author = "Sandrine Peche and Alexander Soshnikov", title = "On the lower bound of the spectral norm of symmetric random matrices with independent entries", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "28:280--28:290", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1376", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1376", abstract = "We show that the spectral radius of an $ N \times N $ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from below by $ 2 \sigma - o(N^{-6 / 11 + \varepsilon }), $ where $ \sigma^2 $ is the variance of the matrix entries and $ \varepsilon $ is an arbitrary small positive number. Combining with our previous result from [7], this proves that for any $ \varepsilon > 0, \ $ one has $ \| A_N \| = 2 \sigma + o(N^{-6 / 11 + \varepsilon }) $ with probability going to $1$ as $ N \to \infty $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Wigner random matrices, spectral norm", } @Article{Holmes:2008:EIA, author = "Mark Holmes and Remco van der Hofstad and Gordon Slade", title = "An extension of the inductive approach to the lace expansion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "29:291--29:301", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1377", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1377", abstract = "We extend the inductive approach to the lace expansion, previously developed to study models with critical dimension 4, to be applicable more generally. In particular, the result of this note has recently been used to prove Gaussian asymptotic behaviour for the Fourier transform of the two-point function for sufficiently spread-out lattice trees in dimensions $ d > 8 $, and it is potentially also applicable to percolation in dimensions $ d > 6 $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "induction; Lace expansion; lattice trees; percolation", } @Article{Kabluchko:2008:ECR, author = "Zakhar Kabluchko and Axel Munk", title = "Exact Convergence Rate for the Maximum of Standardized {Gaussian} Increments", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "30:302--30:310", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1380", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1380", abstract = "We prove an almost sure limit theorem on the exact convergence rate of the maximum of standardized Gaussian random walk increments. This gives a more precise version of Shao's theorem ({\em Shao, Q.-M., 1995. On a conjecture of R{\'e}v{\'e}sz. Proc. Amer. Math. Soc. {\bf 123}, 575--582}) in the Gaussian case.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "standardized increments, Gaussian random walk, multiscale statistic, L{\'e}vy's continuity modulus, integral test, almost sure limit theorem", } @Article{Morris:2008:SGI, author = "Ben Morris", title = "Spectral gap for the interchange process in a box", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "31:311--31:318", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1381", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1381", abstract = "We show that the spectral gap for the interchange process (and the symmetric exclusion process) in a $d$-dimensional box of side length $L$ is asymptotic to $ \pi^2 / L^2$. This gives more evidence in favor of Aldous's conjecture that in any graph the spectral gap for the interchange process is the same as the spectral gap for a corresponding continuous-time random walk. Our proof uses a technique that is similar to that used by Handjani and Jungreis, who proved that Aldous's conjecture holds when the graph is a tree.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "spectral gap, interchange process", } @Article{Vovk:2008:CTT, author = "Vladimir Vovk", title = "Continuous-time trading and the emergence of volatility", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "32:319--32:324", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1383", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1383", abstract = "This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of non-constant price processes has to be 2, as in the case of continuous martingales.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "continuous time; game-theoretic probability; strong variation exponent", } @Article{Song:2008:RBS, author = "Renming Song and Zoran Vondracek", title = "On the relationship between subordinate killed and killed subordinate processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "33:325--33:336", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1388", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1388", abstract = "We study the precise relationship between the subordinate killed and killed subordinate processes in the case of an underlying Hunt process, and show that, under minimal conditions, the former is a subprocess of the latter obtained by killing at a terminal time. Moreover, we also show that the killed subordinate process can be obtained by resurrecting the subordinate killed one at most countably many times.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Markov process, subordination, killing, resurrection", } @Article{Guillotin-Plantard:2008:FLT, author = "Nadine Guillotin-Plantard and Arnaud {Le Ny}", title = "A functional limit theorem for a 2d-random walk with dependent marginals", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "34:337--34:351", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1386", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1386", abstract = "We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to different normalizations in the functional limit theorem, with a non-Gaussian horizontal behavior. We also prove that the horizontal and vertical components are not asymptotically independent.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random walks, random environments, random sceneries", } @Article{Gobet:2008:SEC, author = "Emmanuel Gobet and C{\'e}line Labart", title = "Sharp estimates for the convergence of the density of the {Euler} scheme in small time", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "35:352--35:363", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1393", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1393", abstract = "In this work, we approximate a diffusion process by its Euler scheme and we study the convergence of the density of the marginal laws. We improve previous estimates especially for small time.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Euler scheme; Malliavin calculus; rate of convergence; stochastic differential equation", } @Article{Marcus:2008:IDG, author = "Michael Marcus and Jay Rosen", title = "Infinite Divisibility of {Gaussian} Squares with Non-zero Means", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "36:364--36:376", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1389", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1389", abstract = "We give necessary and sufficient conditions for a Gaussian vector with non-zero mean, to have infinitely divisible squares for all scalar multiples of the mean, and show how the this vector is related to the local times of a Markov chain determined by the covariance matrix of the Gaussian vector. Our results add to results of Griffiths, Bapat, Eisenbaum and Kaspi.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Gaussian vectors, infinite divisibility, Markov chains", } @Article{Pete:2008:NPI, author = "Gabor Pete", title = "A note on percolation on {$ Z^d $}: isoperimetric profile via exponential cluster repulsion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "37:377--37:392", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1390", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1390", abstract = "We show that for all $ p > p_c(\mathbb {Z}^d) $ percolation parameters, the probability that the cluster of the origin is finite but has at least $t$ vertices at distance one from the infinite cluster is exponentially small in $t$. We use this to give a short proof of the strongest version of the important fact that the isoperimetric profile of the infinite cluster basically coincides with the profile of the original lattice. This implies, e.g., that simple random walk on the largest cluster of a finite box $ [ - n, n]^d$ with high probability has $ L^\infty $-mixing time $ \Theta (n^2)$, and that the heat kernel (return probability) on the infinite cluster a.s. decays like $ p_n(o, o) = O(n^{-d / 2})$. Versions of these results have been proven by Benjamini and Mossel (2003), Mathieu and Remy (2004), Barlow (2004) and Rau (2006). For general infinite graphs, we prove that anchored isoperimetric properties survive supercritical percolation, provided that the probability of the cluster of the origin being finite with large boundary decays rapidly; this is the case for a large class of graphs when $p$ is close to 1. As an application (with the help of some entropy inequalities), we give a short conceptual proof of a theorem of Angel, Benjamini, Berger and Peres (2006): the infinite percolation cluster of a wedge in $ \mathbb {Z}^3$ is a.s. transient whenever the wedge itself is transient.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Flury:2008:NBL, author = "Markus Flury", title = "A note on the ballistic limit of random motion in a random potential", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "38:393--38:400", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1394", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1394", abstract = "It has been shown that certain types of random walks in random potentials and Brownian motion in Poissonian potentials undergo a phase transition from sub-ballistic to ballistic behavior when the strength of the underlying drift is increased. The ballistic behavior has been manifested by indicating a limiting area for the normalized motion. In the present article, we provide a refined description of this limiting area with a further development for the case of rotation invariant Poissonian potentials.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "RWRP, random walk, random potential, Brownian motion, Poissonian potential, ballistic phase, ballistic limit", } @Article{Hofmann-Credner:2008:WTR, author = "Katrin Hofmann-Credner and Michael Stolz", title = "{Wigner} theorems for random matrices with dependent entries: Ensembles associated to symmetric spaces and sample covariance matrices", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "39:401--39:414", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1395", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1395", abstract = "It is a classical result of Wigner that for an Hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this paper, we prove analogs of Wigner's theorem for random matrices taken from all infinitesimal versions of classical symmetric spaces. This is a class of models which contains those studied by Wigner and Dyson, along with seven others arising in condensed matter physics. Like Wigner's, our results are universal in that they only depend on certain assumptions about the moments of the matrix entries, but not on the specifics of their distributions. What is more, we allow for a certain amount of dependence among the matrix entries, in the spirit of a recent generalization of Wigner's theorem, due to Schenker and Schulz-Baldes. As a byproduct, we obtain a universality result for sample covariance matrices with dependent entries.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "random matrices, symmetric spaces, semicircle law, Wigner, Marcenko-Pastur, Wishart, sample covariance matrices, dependent random variables, density of states, universality", } @Article{Kargin:2008:AGS, author = "Vladislav Kargin", title = "On Asymptotic Growth of the Support of Free Multiplicative Convolutions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "40:415--40:421", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1396", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1396", abstract = "Let $ \mu $ be a compactly supported probability measure on $ \mathbb {R}^+ $ with expectation $1$ and variance $ V.$ Let $ \mu_n$ denote the $n$-time free multiplicative convolution of measure $ \mu $ with itself. Then, for large $n$ the length of the support of $ \mu_n$ is asymptotically equivalent to $ e V n$, where $e$ is the base of natural logarithms, $ e = 2.71 \ldots $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Free probability, free multiplicative convolution", } @Article{Luschgy:2008:MEL, author = "Harald Luschgy and Gilles Pag{\`e}s", title = "Moment estimates for {L{\'e}vy} Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "41:422--41:434", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1397", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1397", abstract = "For real L{\'e}vy processes $ (X_t)_{t \geq 0} $ having no Brownian component with Blumenthal-Getoor index $ \beta $, the estimate $ E \sup_{s \leq t} |X_s - a_p s|^p \leq C_p t $ for every $ t \in [0, 1] $ and suitable $ a_p \in R $ has been established by Millar for $ \beta < p \leq 2 $ provided $ X_1 \in L^p $. We derive extensions of these estimates to the cases $ p > 2 $ and $ p \leq \beta $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "alpha-stable process; L{\'e}vy measure; L{\'e}vy process increment; Meixner process.; Normal Inverse Gaussian process; tempered stable process", } @Article{Kosters:2008:SOC, author = "Holger K{\"o}sters", title = "On the Second-Order Correlation Function of the Characteristic Polynomial of a Real Symmetric {Wigner} Matrix", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "42:435--42:447", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1400", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1400", abstract = "We consider the asymptotic behaviour of the second-order correlation function of the characteristic polynomial of a real symmetric random matrix. Our main result is that the existing result for a random matrix from the Gaussian Orthogonal Ensemble, obtained by Br{\'e}zin and Hikami (2001), essentially continues to hold for a general real symmetric Wigner matrix. To obtain this result, we adapt the approach by G{\"o}tze and K{\"o}sters (2008), who proved the analogous result for the Hermitian case.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Alberts:2008:IPC, author = "Tom Alberts and Michael Kozdron", title = "Intersection probabilities for a chordal {SLE} path and a semicircle", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "43:448--43:460", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1399", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1399", abstract = "We derive a number of estimates for the probability that a chordal SLE$_\kappa $ path in the upper half plane $ \mathbb {H}$ intersects a semicircle centred on the real line. We prove that if $ 0 < \kappa < 8$ and $ \gamma : [0, \infty) \to \overline {\mathbb {H}}$ is a chordal SLE$_\kappa $ in $ \mathbb {H}$ from $0$ to $ \infty $, then $ P \{ \gamma [0, \infty) \cap \mathcal {C}(x; r x) \neq \emptyset \} \asymp r^{4a - 1}$ where $ a = 2 / \kappa $ and $ \mathcal {C}(x; r x)$ denotes the semicircle centred at $ x > 0$ of radius $ r x$, $ 00$. For $ 4 < \kappa < 8$, we also estimate the probability that an entire semicircle on the real line is swallowed at once by a chordal SLE$_\kappa $ path in $ \mathbb {H}$ from $0$ to $ \infty $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Hausdorff dimension; intersection probability; restriction property; Schramm-Loewner evolution; Schwarz-Christoffel transformation; swallowing time", } @Article{Goldschmidt:2008:FRP, author = "Christina Goldschmidt and James Martin and Dario Spano", title = "Fragmenting random permutations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "44:461--44:474", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1402", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1402", abstract = "{\bf Problem 1.5.7 from Pitman's Saint-Flour lecture notes:} Does there exist for each $n$ a fragmentation process $ (\Pi_{n, k}, 1 \leq k \leq n)$ such that $ \Pi_{n, k}$ is distributed like the partition generated by cycles of a uniform random permutation of $ \{ 1, 2, \ldots, n \} $ conditioned to have $k$ cycles? We show that the answer is yes. We also give a partial extension to general exchangeable Gibbs partitions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Fragmentation process, random permutation, Gibbs partition, Chinese restaurant process", } @Article{Stenflo:2008:PSL, author = "{\"O}rjan Stenflo", title = "Perfect sampling from the limit of deterministic products of stochastic matrices", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "45:474--45:481", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1409", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1409", abstract = "We illustrate how a technique from the theory of random iterations of functions can be used within the theory of products of matrices. Using this technique we give a simple proof of a basic theorem about the asymptotic behavior of (deterministic) ``backwards products'' of row-stochastic matrices and present an algorithm for perfect sampling from the limiting common row-vector (interpreted as a probability-distribution).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Perfect sampling, Stochastic matrices, Markov Chain Monte Carlo, Iterated Function Systems", } @Article{Breton:2008:EBN, author = "Jean-Christophe Breton and Ivan Nourdin", title = "Error bounds on the non-normal approximation of {Hermite} power variations of fractional {Brownian} motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "46:482--46:493", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1415", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1415", abstract = "Let $ q \geq 2 $ be a positive integer, $B$ be a fractional Brownian motion with Hurst index $ H \in (0, 1)$, $Z$ be an Hermite random variable of index $q$, and $ H_q$ denote the $q$ th Hermite polynomial. For any $ n \geq 1$, set $ V_n = \sum_{k = 0}^{n - 1} H_q(B_{k + 1} - B_k)$. The aim of the current paper is to derive, in the case when the Hurst index verifies $ H > 1 - 1 / (2 q)$, an upper bound for the total variation distance between the laws $ \mathscr {L}(Z_n)$ and $ \mathscr {L}(Z)$, where $ Z_n$ stands for the correct renormalization of $ V_n$ which converges in distribution towards $Z$. Our results should be compared with those obtained recently by Nourdin and Peccati (2007) in the case where $ H < 1 - 1 / (2 q)$, corresponding to the case where one has normal approximation.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Fractional Brownian motion; Hermite power variation; Hermite random variable; Multiple stochastic integrals; Non-central limit theorem; Total variation distance", } @Article{Millan:2008:RGL, author = "Juan Carlos Pardo Millan", title = "On the rate of growth of {L{\'e}vy} processes with no positive jumps conditioned to stay positive", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "47:494--47:506", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1414", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1414", abstract = "In this note, we study the asymptotic behaviour of L{\'e}vy processes with no positive jumps conditioned to stay positive and some related processes. In particular, we establish an integral test for the lower envelope at $0$ and at $ + \infty $ and an analogue of Khintchin's law of the iterated logarithm at 0 and at $ + \infty $, for the upper envelope of the reflected process at its future infimum.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "L{\'e}vy processes conditioned to stay positive, Future infimum process, First and last passage times, Occupation times, Rate of growth, Integral tests.", } @Article{Yukich:2008:LTM, author = "Joseph Yukich", title = "Limit theorems for multi-dimensional random quantizers", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "48:507--48:517", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1418", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1418", abstract = "We consider the $r$-th power quantization error arising in the optimal approximation of a $d$-dimensional probability measure $P$ by a discrete measure supported by the realization of $n$ i.i.d. random variables $ X_1, \ldots {}, X_n$. For all $ d \geq 1$ and $ r \in (0, \infty)$ we establish mean and variance asymptotics as well as central limit theorems for the $r$-th power quantization error. Limiting means and variances are expressed in terms of the densities of $P$ and $ X_1$. Similar convergence results hold for the random point measures arising by placing at each $ X_i, 1 \leq i \leq n, $ a mass equal to the local distortion.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "central limit theorems; laws of large numbers; Quantization; stabilization", } @Article{Jiang:2008:DRF, author = "Thomas Jiang and Kun-Lin Kuo", title = "Distribution of a random functional of a {Ferguson--Dirichlet} process over the unit sphere", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "49:518--49:525", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1416", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1416", abstract = "Jiang, Dickey, and Kuo [12] gave the multivariate c-characteristic function and showed that it has properties similar to those of the multivariate Fourier transformation. We first give the multivariate c-characteristic function of a random functional of a Ferguson--Dirichlet process over the unit sphere. We then find out its probability density function using properties of the multivariate c-characteristic function. This new result would generalize that given by [11].", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "c-characteristic function; Ferguson--Dirichlet process", } @Article{Abreu:2008:FGG, author = "Victor Perez Abreu and Noriyoshi Sakuma", title = "Free Generalized Gamma Convolutions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "50:526--50:539", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1413", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1413", abstract = "The so-called Bercovici-Pata bijection maps the set of classical infinitely divisible laws to the set of free infinitely divisible laws. The purpose of this work is to study the free infinitely divisible laws corresponding to the classical Generalized Gamma Convolutions (GGC). Characterizations of their free cumulant transforms are derived as well as free integral representations with respect to the free Gamma process. A random matrix model for free GGC is built consisting of matrix random integrals with respect to a classical matrix Gamma process. Nested subclasses of free GGC are shown to converge to the free stable class of distributions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Free probability; generalized gamma convolutions; infinitely divisible distribution; random matrices", } @Article{Jagers:2008:GBP, author = "Peter Jagers and Andreas Lager{\aa}s", title = "General branching processes conditioned on extinction are still branching processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "51:540--51:547", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1419", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1419", abstract = "It is well known that a simple, supercritical Bienaym{\'e}-Galton--Watson process turns into a subcritical such process, if conditioned to die out. We prove that the corresponding holds true for general, multi-type branching, where child-bearing may occur at different ages, life span may depend upon reproduction, and the whole course of events is thus affected by conditioning upon extinction.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Crump-Mode-Jagers process; extinction; general branching process; multi-type branching process; subcritical; supercritical", } @Article{Lalley:2008:OCM, author = "Steven Lalley and George Kordzakhia", title = "An oriented competition model on {$ Z_+^2 $}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "52:548--52:561", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1422", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1422", abstract = "We consider a two-type oriented competition model on the first quadrant of the two-dimensional integer lattice. Each vertex of the space may contain only one particle of either Red type or Blue type. A vertex flips to the color of a randomly chosen southwest nearest neighbor at exponential rate 2. At time zero there is one Red particle located at $ (1, 0) $ and one Blue particle located at $ (0, 1) $. The main result is a partial shape theorem: Denote by $ R (t) $ and $ B (t) $ the red and blue regions at time $t$. Then (i) eventually the upper half of the unit square contains no points of $ B (t) / t$, and the lower half no points of $ R (t) / t$; and (ii) with positive probability there are angular sectors rooted at $ (1, 1)$ that are eventually either red or blue. The second result is contingent on the uniform curvature of the boundary of the corresponding Richardson shape.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "competition, shape theorem, first passage percolation", } @Article{VanHandel:2008:DTN, author = "Ramon {Van Handel}", title = "Discrete time nonlinear filters with informative observations are stable", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "53:562--53:575", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1423", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1423", abstract = "The nonlinear filter associated with the discrete time signal-observation model $ (X_k, Y_k) $ is known to forget its initial condition as $ k \to \infty $ regardless of the observation structure when the signal possesses sufficiently strong ergodic properties. Conversely, it stands to reason that if the observations are sufficiently informative, then the nonlinear filter should forget its initial condition regardless of any properties of the signal. We show that for observations of additive type $ Y_k = h(X_k) + \xi_k $ with invertible observation function $h$ (under mild regularity assumptions on $h$ and on the distribution of the noise $ \xi_k$), the filter is indeed stable in a weak sense without any assumptions at all on the signal process. If the signal satisfies a uniform continuity assumption, weak stability can be strengthened to stability in total variation.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "asymptotic stability; hidden Markov models; nonlinear filtering; prediction", } @Article{Muller:2008:RBM, author = "Sebastian M{\"u}ller", title = "Recurrence for branching {Markov} chains", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "54:576--54:605", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1424", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1424", abstract = "The question of recurrence and transience of branching Markov chains is more subtle than for ordinary Markov chains; they can be classified in transience, weak recurrence, and strong recurrence. We review criteria for transience and weak recurrence and give several new conditions for weak recurrence and strong recurrence. These conditions make a unified treatment of known and new examples possible and provide enough information to distinguish between weak and strong recurrence. This represents a step towards a general classification of branching Markov chains. In particular, we show that in homogeneous cases weak recurrence and strong recurrence coincide. Furthermore, we discuss the generalization of positive and null recurrence to branching Markov chains and show that branching random walks on $Z$ are either transient or positive recurrent.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "spectral radius, branching Markov chains, recurrence, transience, strong recurrence, positive recurrence", } @Article{Kink:2008:MZS, author = "Peter Kink", title = "A martingale on the zero-set of a holomorphic function", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "55:606--55:613", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1425", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1425", abstract = "We give a simple probabilistic proof of the classical fact from complex analysis that the zeros of a holomorphic function of several variables are never isolated and that they are not contained in any compact set. No facts from complex analysis are assumed other than the Cauchy-Riemann definition. From stochastic analysis only the Ito formula and the standard existence theorem for stochastic differential equations are required.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "complex martingales; stochastic differential equations", } @Article{Burdzy:2008:MPP, author = "Krzysztof Burdzy and David White", title = "{Markov} processes with product-form stationary distribution", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "56:614--56:627", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1428", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1428", abstract = "We consider a continuous time Markov process $ (X, L) $, where $X$ jumps between a finite number of states and $L$ is a piecewise linear process with state space $ \mathbb {R}^d$. The process $L$ represents an {"inert} {drift"} or {"reinforcement."} We find sufficient and necessary conditions for the process $ (X, L)$ to have a stationary distribution of the product form, such that the marginal distribution of $L$ is Gaussian. We present a number of conjectures for processes with a similar structure but with continuous state spaces.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Markov process, stationary distribution, inert drift", } @Article{Bertail:2008:EBM, author = "Patrice Bertail and Emmanuelle Gautherat and Hugo Harari-Kermadec", title = "Exponential bounds for multivariate self-normalized sums", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "57:628--57:640", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1430", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1430", abstract = "In a non-parametric framework, we establish some non-asymptotic bounds for self-normalized sums and quadratic forms in the multivariate case for symmetric and general random variables. This bounds are entirely explicit and essentially depends in the general case on the kurtosis of the Euclidean norm of the standardized random variables.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Exponential inequalities; Hoeffding inequality.; multivariate; Self-normalization", } @Article{Chigansky:2008:DBM, author = "Pavel Chigansky and Fima Klebaner", title = "Distribution of the {Brownian} motion on its way to hitting zero", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "58:641--58:648", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1432", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1432", abstract = "For the one-dimensional Brownian motion $ B = (B_t)_{t \geq 0} $, started at $ x > 0 $, and the first hitting time $ \tau = \inf \{ t \geq 0 : B_t = 0 \} $, we find the probability density of $ B_{u \tau } $ for a $ u \in (0, 1) $, i.e. of the Brownian motion on its way to hitting zero.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Bessel bridge; Brownian bridge; Brownian motion; heavy-tailed distribution; hitting time; scaled Brownian excursion", } @Article{Enriquez:2008:RSS, author = "Nathanael Enriquez and Christophe Sabot and Marc Yor", title = "Renewal series and square-root boundaries for {Bessel} processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "59:649--59:652", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1436", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1436", abstract = "We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical results by Breiman and Shepp, concerning Brownian motion, and recovers by different means, extensions for Bessel processes, obtained independently by Delong and Yor.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Bessel processes, renewal series, exponential functionals, square-root boundaries", } @Article{Peskir:2008:LHT, author = "Goran Peskir", title = "The Law of the Hitting Times to Points by a Stable {L{\'e}vy} Process with No Negative Jumps", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "60:653--60:659", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1431", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1431", abstract = "Let $ X = (X_t)_{t \ge 0} $ be a stable L{\'e}vy process of index $ \alpha \in (1, 2) $ with the L{\'e}vy measure $ \nu (d x) = (c / x^{1 + \alpha }) I_{(0, \infty)}(x) d x $ for $ c > 0 $, let $ x > 0 $ be given and fixed, and let $ \tau_x = \inf \{ t > 0 : X_t = x \} $ denote the first hitting time of $X$ to $x$. Then the density function $ f_{\tau_x}$ of $ \tau_x$ admits the following series representation:\par $$ f_{\tau_x}(t) = \frac {x^{\alpha - 1}}{\pi (\Gamma (\alpha) t)^{2 - 1 / \alpha }} \sum_{n = 1}^\infty \bigg [( - 1)^{n - 1} \sin (\pi / \alpha) \frac {\Gamma (n - 1 / \alpha)}{\Gamma (\alpha n - 1)} \Big (\frac {x^\alpha }{c \Gamma ( - \alpha)t} \Big)^{n - 1} $$ $$ - \sin \Big (\frac {n \pi }{\alpha } \Big) \frac {\Gamma (1 + n / \alpha)}{n!} \Big (\frac {x^\alpha }{c \Gamma ( - \alpha)t} \Big)^{(n + 1) / \alpha - 1} \bigg] $$ for $ t > 0$. In particular, this yields $ f_{\tau_x}(0 +) = 0$ and\par $$ f_{\tau_x}(t) \sim \frac {x^{\alpha - 1}}{\Gamma (\alpha - 1), \Gamma (1 / \alpha)} (c \Gamma ( - \alpha)t)^{-2 + 1 / \alpha } $$ as $ t \rightarrow \infty $. The method of proof exploits a simple identity linking the law of $ \tau_x$ to the laws of $ X_t$ and $ \sup_{0 \le s \le t} X_s$ that makes a Laplace inversion amenable. A simpler series representation for $ f_{\tau_x}$ is also known to be valid when $ x < 0$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stable L{\'e}vy process with no negative jumps, spectrally positive, first hitting time to a point, first passage time over a point, supremum process, a Chapman-Kolmogorov equation of Volterra type, Laplace transform, the Wiener-Hopf factorisation.", } @Article{Osekowski:2008:SIB, author = "Adam Osekowski", title = "Sharp inequality for bounded submartingales and their differential subordinates", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "61:660--61:675", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1433", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1433", abstract = "Let $ \alpha $ be a fixed number from the interval $ [0, 1] $. We obtain the sharp probability bounds for the maximal function of the process which is $ \alpha $-differentially subordinate to a bounded submartingale. This generalizes the previous results of Burkholder and Hammack.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "conditional differential subordination; differential subordination; distribution function; Martingale; submartingale; tail inequality", } @Article{Dumbgen:2008:EBA, author = "Lutz D{\"u}mbgen and Christoph Leuenberger", title = "Explicit Bounds for the Approximation Error in {Benford}'s Law", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "10:99--10:112", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v13-1358", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60E15 (60F99)", MRnumber = "2386066 (2009b:60056)", MRreviewer = "Pieter C. Allaart", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.math.utah.edu/pub/tex/bib/ecp.bib; http://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://arxiv.org/abs/0705.4488; http://ecp.ejpecp.org/article/view/1358; http://weber.math.washington.edu/~ejpecp/ECP/index.php", abstract = "Benford's law states that for many random variables $ X > 0 $ its leading digit $ D = D(X) $ satisfies approximately the equation $ \mathbb {P}(D = d) = \log_{10}(1 + 1 / d) $ for $ d = 1, 2, \ldots, 9 $. This phenomenon follows from another, maybe more intuitive fact, applied to $ Y := \log_{10}X $: For many real random variables $Y$, the remainder $ U := Y - \lfloor Y \rfloor $ is approximately uniformly distributed on $ [0, 1)$. The present paper provides new explicit bounds for the latter approximation in terms of the total variation of the density of $Y$ or some derivative of it. These bounds are an interesting and powerful alternative to Fourier methods. As a by-product we obtain explicit bounds for the approximation error in Benford's law.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Hermite polynomials, Gumbel distribution, Kuiper distance, normal distribution, total variation, uniform distribution, Weibull distribution", } @Article{Dieker:2009:RBM, author = "A. B. Dieker and J. Moriarty", title = "Reflected {Brownian} motion in a wedge: sum-of-exponential stationary densities", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "1:1--1:16", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1437", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1437", abstract = "We give necessary and sufficient conditions for the stationary density of semimartingale reflected Brownian motion in a wedge to be written as a finite sum of terms of exponential product form. Relying on geometric ideas reminiscent of the reflection principle, we give an explicit formula for the density in such cases.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Reflected Brownian motion with drift -- stationary distribution -- reflection principle", } @Article{Osekowski:2009:SMI, author = "Adam Osekowski", title = "Sharp maximal inequality for martingales and stochastic integrals", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "2:17--2:30", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1438", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1438", abstract = "Let $ X = (X_t)_{t \geq 0} $ be a martingale and $ H = (H_t)_{t \geq 0} $ be a predictable process taking values in $ [ - 1, 1] $. Let $Y$ denote the stochastic integral of $H$ with respect to $X$. We show that\par $$ || \sup_{t \geq 0}Y_t||_1 \leq \beta_0 || \sup_{t \geq 0}|X_t|||_1, $$ where $ \beta_0 = 2, 0856 \ldots $ is the best possible. Furthermore, if, in addition, $X$ is nonnegative, then\par $$ || \sup_{t \geq 0}Y_t||_1 \leq \beta_0^+ || \sup_{t \geq 0}X_t||_1, $$ where $ \beta_0^+= \frac {14}{9}$ is the best possible.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Martingale; maximal function; stochastic integral", } @Article{Eckhoff:2009:UMM, author = "Maren Eckhoff and Silke Rolles", title = "Uniqueness of the mixing measure for a random walk in a random environment on the positive integers", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "3:31--3:35", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1441", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1441", abstract = "Consider a random walk in an irreducible random environment on the positive integers. We prove that the annealed law of the random walk determines uniquely the law of the random environment. An application to linearly edge-reinforced random walk is given.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "random walk in a random environment, mixing measure", } @Article{Bjorner:2009:NRF, author = "Anders Bjorner", title = "Note: Random-to-front shuffles on trees", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "4:36--4:41", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1445", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1445", abstract = "A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local ``random-to-front'' reorderings, driven by a probability distribution on subsets of the leaves. The eigenvalues of the transition matrix are determined using Brown's theory of random walk on semigroups.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "eigenvalue; Markov chain; random walk; random-to-front; semigroup; shuffle; tree", } @Article{Haggstrom:2009:STD, author = "Olle H{\"a}ggstr{\"o}m and P{\'e}ter Mester", title = "Some two-dimensional finite energy percolation processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "5:42--5:54", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1446", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1446", abstract = "Some examples of translation invariant site percolation processes on the $ Z^2 $ lattice are constructed, the most far-reaching example being one that satisfies uniform finite energy (meaning that the probability that a site is open given the status of all others is bounded away from 0 and 1) and exhibits a.s. the coexistence of an infinite open cluster and an infinite closed cluster. Essentially the same example shows that coexistence is possible between an infinite open cluster and an infinite closed cluster that are both robust under i.i.d. thinning.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "percolation, uniform finite energy, coexistence", } @Article{Mueller:2009:CBS, author = "Carl Mueller and Zhixin Wu", title = "A connection between the stochastic heat equation and fractional {Brownian} motion, and a simple proof of a result of {Talagrand}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "6:55--6:65", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1403", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", note = "See erratum \cite{Mueller:2012:ECB}.", URL = "http://ecp.ejpecp.org/article/view/1403", abstract = "We give a new representation of fractional Brownian motion with Hurst parameter $ H \leq \frac {1}{2} $ using stochastic partial differential equations. This representation allows us to use the Markov property and time reversal, tools which are not usually available for fractional Brownian motion. We then give simple proofs that fractional Brownian motion does not hit points in the critical dimension, and that it does not have double points in the critical dimension. These facts were already known, but our proofs are quite simple and use some ideas of L{\'e}vy. {\bf An Erratum is available in \url{https://doi.org/10.1214/ECP.v17-1774} ECP volume {\bf 17} paper number 8.}", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "heat equation, white noise, stochastic partial differential equations", } @Article{Kendall:2009:BCC, author = "Wilfrid Kendall", title = "{Brownian} couplings, convexity, and shy-ness", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "7:66--7:80", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1417", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1417", abstract = "Benjamini, Burdzy and Chen (2007) introduced the notion of a {\em shy coupling\/}: a coupling of a Markov process such that, for suitable starting points, there is a positive chance of the two component processes of the coupling staying at least a given positive distance away from each other for all time. Among other results, they showed that no shy couplings could exist for reflected Brownian motions in $ C^2 $ bounded convex planar domains whose boundaries contain no line segments. Here we use potential-theoretic methods to extend this Benjamini {\em et al.\/}(2007) result (a) to all bounded convex domains (whether planar and smooth or not) whose boundaries contain no line segments, (b) to all bounded convex planar domains regardless of further conditions on the boundary.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion, coupling", } @Article{Deijfen:2009:SRG, author = "Maria Deijfen", title = "Stationary random graphs with prescribed iid degrees on a spatial {Poisson} process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "8:81--8:89", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1448", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1448", abstract = "Let $ [\mathcal {P}] $ be the points of a Poisson process on $ R^d $ and $F$ a probability distribution with support on the non-negative integers. Models are formulated for generating translation invariant random graphs with vertex set $ [\mathcal {P}]$ and iid vertex degrees with distribution $F$, and the length of the edges is analyzed. The main result is that finite mean for the total edge length per vertex is possible if and only if $F$ has finite moment of order $ (d + 1) / d$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random graphs, degree distribution, Poisson process, stable matching, stationary model", } @Article{Kovchegov:2009:OPB, author = "Yevgeniy Kovchegov", title = "Orthogonality and probability: beyond nearest neighbor transitions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "9:90--9:103", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1447", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1447", abstract = "In this article, we will explore why Karlin-McGregor method of using orthogonal polynomials in the study of Markov processes was so successful for one dimensional nearest neighbor processes, but failed beyond nearest neighbor transitions. We will proceed by suggesting and testing possible fixtures.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "reversible Markov chains, orthogonal polynomials, Karlin-McGregor representation", } @Article{Holmes:2009:SLS, author = "Mark Holmes", title = "The scaling limit of senile reinforced random walk", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "10:104--10:115", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1449", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1449", abstract = "This paper proves that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean. We show that under suitable conditions, when T has heavy tails the scaling limit is the so-called fractional kinetics process, a random time-change of Brownian motion. The proof uses the standard tools of time-change and invariance principles for additive functionals of Markov chains.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Privault:2009:MIS, author = "Nicolas Privault", title = "Moment identities for {Skorohod} integrals on the {Wiener} space and applications", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "11:116--11:121", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1450", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1450", abstract = "We prove a moment identity on the Wiener space that extends the Skorohod isometry to arbitrary powers of the Skorohod integral on the Wiener space. As simple consequences of this identity we obtain sufficient conditions for the Gaussianity of the law of the Skorohod integral and a recurrence relation for the moments of second order Wiener integrals. We also recover and extend the sufficient conditions for the invariance of the Wiener measure under random rotations given in A. S. {\"U}st{\"u}nel and M. Zakai {\em Prob. Th. Rel. Fields\/} {\bf 103} (1995), 409--429.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Malliavin calculus, Skorohod integral, Skorohod isometry, Wiener measure, random isometries.", } @Article{vanderHofstad:2009:LLT, author = "Remco van der Hofstad and Wouter Kager and Tobias M{\"u}ller", title = "A local limit theorem for the critical random graph", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "12:122--12:131", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1451", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1451", abstract = "We consider the limit distribution of the orders of the $k$ largest components in the Erdos-R{\'e}nyi random graph inside the {"critical} {window"} for arbitrary $k$. We prove a local limit theorem for this joint distribution and derive an exact expression for the joint probability density function.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random graphs", } @Article{Marchal:2009:STE, author = "Philippe Marchal", title = "Small time expansions for transition probabilities of some {L{\'e}vy} processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "13:132--13:142", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1452", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1452", abstract = "We show that there exist L{\'e}vy processes $ (X_t, t \geq 0) $ and reals $ y > 0 $ such that for small $t$, the probability $ P(X_t > y)$ has an expansion involving fractional powers or more general functions of $t$. This constrasts with previous results giving polynomial expansions under additional assumptions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "L{\'e}vy process, transition probability", } @Article{Janssen:2009:ESM, author = "A. J. E. M. Janssen and J. S. H. {Van Leeuwaarden}", title = "Equidistant sampling for the maximum of a {Brownian} motion with drift on a finite horizon", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "14:143--14:150", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1453", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1453", abstract = "A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian motion and its sampled version, an expansion is derived with coefficients in terms of the drift, the Riemann zeta function and the normal distribution function.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "equidistant sampling of Brownian motion; Euler-Maclaurin summation; finite horizon; Gaussian random walk; maximum; Riemann zeta function", } @Article{Duquesne:2009:EPH, author = "Thomas Duquesne", title = "An elementary proof of {Hawkes}'s conjecture on {Galton--Watson} trees", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "15:151--15:164", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1454", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1454", abstract = "In 1981, J. Hawkes conjectured the exact form of the Hausdorff gauge function for the boundary of supercritical Galton--Watson trees under a certain assumption on the tail at infinity of the total mass of the branching measure. Hawkes's conjecture has been proved by T. Watanabe in 2007 as well as other precise results on fractal properties of the boundary of Galton--Watson trees. The goal of this paper is to provide an elementary proof of Hawkes's conjecture under a less restrictive assumption than in T. Watanabe's paper, by use of size-biased Galton--Watson trees introduced by Lyons, Pemantle and Peres in 1995.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "boundary; branching measure; exact Hausdorff measure; Galton--Watson tree; size-biased tree", } @Article{Sheu:2009:NBM, author = "Yuan-Chung Sheu and Yu-Ting Chen", title = "A note on $r$-balayages of matrix-exponential {L{\'e}vy} processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "16:165--16:175", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1456", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1456", abstract = "In this note we give semi-explicit solutions for $r$-balayages of matrix-exponential-L{\'e}vy processes. To this end, we turn to an identity for the joint Laplace transform of the first entry time and the undershoot and a semi-explicit solution of the negative Wiener-Hopf factor. Our result is closely related to the works by Mordecki in [11], Asmussen, Avram and Pistorius in [3], Chen, Lee and Sheu in [7], and many others", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Meckes:2009:QAG, author = "Elizabeth Meckes", title = "Quantitative asymptotics of graphical projection pursuit", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "17:176--17:185", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1457", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1457", abstract = "There is a result of Diaconis and Freedman which says that, in a limiting sense, for large collections of high-dimensional data most one-dimensional projections of the data are approximately Gaussian. This paper gives quantitative versions of that result. For a set of $n$ deterministic vectors $ \{ x_i \} $ in $ R^d$ with $n$ and $d$ fixed, let $ \theta $ be a random point of the sphere and let $ \mu_\theta $ denote the random measure which puts equal mass at the projections of each of the $ x_i$ onto the direction $ \theta $. For a fixed bounded Lipschitz test function $f$, an explicit bound is derived for the probability that the integrals of $f$ with respect to $ \mu_\theta $ and with respect to a suitable Gaussian distribution differ by more than $ \epsilon $. A bound is also given for the probability that the bounded-Lipschitz distance between these two measures differs by more than $ \epsilon $, which yields a lower bound on the waiting time to finding a non-Gaussian projection of the $ x_i$, if directions are tried independently and uniformly.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Projection pursuit, concentration inequalities, Stein's method, Lipschitz distance", } @Article{Lopez-Garcia:2009:CDL, author = "Marcos Lopez-Garcia", title = "Characterization of distributions with the length-bias scaling property", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "18:186--18:191", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1458", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1458", abstract = "This paper characterizes the density functions of absolutely continuous positive random variables with finite expectation whose respective distribution functions satisfy the so-called length-bias scaling property.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Length-bias scaling property, Indeterminate moment problem, theta function", } @Article{Kuhn:2009:NSI, author = "Christoph K{\"u}hn and Maximilian Stroh", title = "A note on stochastic integration with respect to optional semimartingales", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "19:192--19:201", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1465", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1465", abstract = "In this note we discuss the extension of the elementary stochastic Ito-integral w.r.t. an optional semimartingale. The paths of an optional semimartingale possess limits from the left and from the right, but may have double jumps. This leads to quite interesting phenomena in integration theory.\par We find a mathematically tractable domain of general integrands. The simple integrands are embedded into this domain. Then, we characterize the integral as the unique continuous and linear extension of the elementary integral and show completeness of the space of integrals. Thus our integral possesses desirable properties to model dynamic trading gains in mathematical finance when security price processes follow optional semimartingales.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "stochastic integration theory, optional semimartingales, dynamic portfolio choice", } @Article{Eisenbaum:2009:OIF, author = "Nathalie Eisenbaum and Alexander Walsh", title = "An optimal {It{\^o}} formula for {L{\'e}vy} processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "20:202--20:209", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1469", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1469", abstract = "Several It{\^o} formulas have been already established for L{\'e}vy processes. We explain according to which criteria they are not {\em optimal\/} and establish an extended It{\^o} formula that satisfies that criteria. The interest, in particular, of this formula is to obtain the explicit decomposition of $ F(X) $, for $X$ L{\'e}vy process and $F$ deterministic function with locally bounded first order Radon-Nikodym derivatives, as the sum of a Dirichlet process and a bounded variation process.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "stochastic calculus, L{\'e}vy process, local time, It{\^o} formula", } @Article{Gao:2009:DIM, author = "Fuqing Gao and Hui Jiang", title = "Deviation inequalities and moderate deviations for estimators of parameters in an {Ornstein--Uhlenbeck} process with linear drift", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "21:210--21:223", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1466", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1466", abstract = "Some deviation inequalities and moderate deviation principles for the maximum likelihood estimators of parameters in an Ornstein--Uhlenbeck process with linear drift are established by the logarithmic Sobolev inequality and the exponential martingale method.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Deviation inequality; logarithmic Sobolev inequality; moderate deviations; Ornstein--Uhlenbeck process", } @Article{Lin:2009:ASL, author = "Fuming Lin", title = "An Almost Sure Limit Theorem For the Maxima of Strongly Dependent {Gaussian} Sequences", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "22:224--22:231", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1461", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1461", abstract = "In this paper, we prove an almost sure limit theorem for the maxima of strongly dependent Gaussian sequences under some mild conditions. The result is an expansion of the weakly dependent result of E. Csaki and K. Gonchigdanzan.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Almost sure central limit theorem, Strongly dependent sequence, Logarithmic average", } @Article{Wang:2009:FEO, author = "Jian Wang", title = "First Eigenvalue of One-dimensional Diffusion Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "23:232--23:244", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1464", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1464", abstract = "We consider the first Dirichlet eigenvalue of diffusion operators on the half line. A criterion for the equivalence of the first Dirichlet eigenvalue with respect to the maximum domain and that to the minimum domain is presented. We also describe the relationships between the first Dirichlet eigenvalue of transient diffusion operators and the standard Muckenhoupt's conditions for the dual weighted Hardy inequality. Pinsky's result [17] and Chen's variational formulas [8] are reviewed, and both provide the original motivation for this research.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "First Dirichlet eigenvalue, Hardy inequality, variational formula, transience, recurrence, diffusion operators", } @Article{Dolgopyat:2009:NPA, author = "Dmitry Dolgopyat and Carlangelo Liverani", title = "Non-perturbative approach to random walk in {Markovian} environment", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "24:245--24:251", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1467", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1467", abstract = "We prove the CLT for a random walk in a dynamical environment where the states of the environment at different sites are independent Markov chains.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Central Limit Theorem; Gibbs measures; random environment; Random walk", } @Article{Balan:2009:NFK, author = "Raluca Balan", title = "A Note on a {Feynman--Kac}-Type Formula", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "25:252--25:260", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1468", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1468", abstract = "In this article, we establish a probabilistic representation for the second-order moment of the solution of stochastic heat equation, with multiplicative noise, which is fractional in time and colored in space. This representation is similar to the one given in Dalang, Mueller and Tribe (2008) in the case of an s.p.d.e. driven by a Gaussian noise, which is white in time. Unlike the formula of Dalang, Mueller and Tribe (2008) , which is based on the usual Poisson process, our representation is based on the planar Poisson process, due to the fractional component of the noise.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "fractional Brownian motion, stochastic heat equation, Feynman--Kac formula, planar Poisson process", } @Article{Wastlund:2009:EPL, author = "Johan W{\"a}stlund", title = "An easy proof of the $ \zeta (2) $ limit in the random assignment problem", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "26:261--26:269", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1475", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1475", abstract = "The edges of the complete bipartite graph $ K_{n, n} $ are given independent exponentially distributed costs. Let $ C_n $ be the minimum total cost of a perfect matching. It was conjectured by M. M{\'e}zard and G. Parisi in 1985, and proved by D. Aldous in 2000, that $ C_n $ converges in probability to $ \pi^2 / 6 $. We give a short proof of this fact, consisting of a proof of the exact formula $ 1 + 1 / 4 + 1 / 9 + \dots + 1 / n^2 $ for the expectation of $ C_n $, and a $ O(1 / n) $ bound on the variance.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "minimum, matching, graph, exponential", } @Article{Hough:2009:TTR, author = "Robert Hough", title = "Tesselation of a triangle by repeated barycentric subdivision", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "27:270--27:277", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1471", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1471", abstract = "Under iterated barycentric subdivision of a triangle, most triangles become flat in the sense that the largest angle tends to $ \pi $. By analyzing a random walk on $ S L_2 (\mathbb {R}) $ we give asymptotics with explicit constants for the number of flat triangles and the degree of flatness at a given stage of subdivision. In particular, we prove analytical bounds for the upper Lyapunov constant of the walk.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Barycentric subdivision; random walk on a group", } @Article{Tudor:2009:HRS, author = "Ciprian Tudor", title = "{Hsu--Robbins} and {Spitzer}'s theorems for the variations of fractional {Brownian} motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "28:278--28:289", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1481", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1481", abstract = "Using recent results on the behavior of multiple Wiener-It{\^o} integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "multiple stochastic integrals, selfsimilar processes, fractional Brownian motion, Hermite processes, limit theorems, Stein's method.", } @Article{Biggins:2009:LDR, author = "J. D. Biggins and D. B. Penman", title = "Large deviations in randomly coloured random graphs", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "29:290--29:301", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1478", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1478", abstract = "Models of random graphs are considered where the presence or absence of an edge depends on the random types (colours) of its vertices, so that whether or not edges are present can be dependent. The principal objective is to study large deviations in the number of edges. These graphs provide a natural example with two different non-degenerate large deviation regimes, one arising from large deviations in the colourings followed by typical edge placement and the other from large deviation in edge placement. A secondary objective is to illustrate the use of a general result on large deviations for mixtures.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "large deviations, mixture, rate function, random graphs", } @Article{Bernardin:2009:MNP, author = "Fr{\'e}d{\'e}ric Bernardin and Mireille Bossy and Miguel Martinez and Denis Talay", title = "On mean numbers of passage times in small balls of discretized {It{\^o}} processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "30:302--30:316", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1479", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1479", abstract = "The aim of this note is to prove estimates on mean values of the number of times that It{\^o} processes observed at discrete times visit small balls in $ \mathbb {R}^d $. Our technique, in the innite horizon case, is inspired by Krylov's arguments in [2, Chap.2]. In the finite horizon case, motivated by an application in stochastic numerics, we discount the number of visits by a locally exploding coefficient, and our proof involves accurate properties of last passage times at 0 of one dimensional semimartingales.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Diffusion processes, sojourn times, estimates, discrete times", } @Article{Duquesne:2009:RRI, author = "Thomas Duquesne and Jean-Fran{\c{c}}ois {Le Gall}", title = "On the re-rooting invariance property of {L{\'e}vy} trees", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "31:317--31:326", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1484", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1484", abstract = "We prove a strong form of the invariance under re-rooting of the distribution of the continuous random trees called L{\'e}vy trees. This expends previous results due to several authors.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "continuous tree; re-rooting, L{\'e}vy process; stable tree", } @Article{Khorunzhiy:2009:UBE, author = "Oleksiy Khorunzhiy and Jean-Fran{\c{c}}ois Marckert", title = "Uniform bounds for exponential moment of maximum of a {Dyck} path", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "32:327--32:333", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1486", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1486", abstract = "Let us consider the maximum $ M(D) $ of a Dyck path $D$ chosen uniformly in the set of Dyck paths with $ 2 n$ steps. We prove that the exponential moment of $ M(D)$ normalized by the square root of $n$ is bounded in the limit of infinite $n$. This uniform bound justifies an assumption used in literature to prove certain estimates of high moments of large random matrices.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Bernoulli bridge; Dyck paths; random matrices", } @Article{Guntuboyina:2009:CSM, author = "Adityanand Guntuboyina and Hannes Leeb", title = "Concentration of the spectral measure of large {Wishart} matrices with dependent entries", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "33:334--33:342", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1483", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1483", abstract = "We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Wishart matrices, concentration inequalities, spectral measure", } @Article{Janson:2009:SRM, author = "Svante Janson", title = "Standard representation of multivariate functions on a general probability space", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "34:343--34:346", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1477", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1477", abstract = "It is well-known that a random variable, i.e. a function defined on a probability space, with values in a Borel space, can be represented on the special probability space consisting of the unit interval with Lebesgue measure. We show an extension of this to multivariate functions. This is motivated by some recent constructions of random graphs.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Borel space; random graphs", } @Article{Yadin:2009:REM, author = "Ariel Yadin", title = "Rate of Escape of the Mixer Chain", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "35:347--35:357", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1474", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1474", abstract = "The mixer chain on a graph $G$ is the following Markov chain. Place tiles on the vertices of $G$, each tile labeled by its corresponding vertex. A {"mixer"} moves randomly on the graph, at each step either moving to a randomly chosen neighbor, or swapping the tile at its current position with some randomly chosen adjacent tile. We study the mixer chain on $ \mathbb {Z}$, and show that at time $t$ the expected distance to the origin is $ t^{3 / 4}$, up to constants. This is a new example of a random walk on a group with rate of escape strictly between $ t^{1 / 2}$ and $t$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Maejima:2009:NNC, author = "Makoto Maejima and Genta Nakahara", title = "A note on new classes of infinitely divisible distributions on $ \mathbb {R}^d $", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "36:358--36:371", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1487", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1487", abstract = "This paper introduces and studies a family of new classes of infinitely divisible distributions on $ \mathbb {R}^d $ with two parameters. Depending on parameters, these classes connect the Goldie-Steutel-Bondesson class and the class of generalized type $G$ distributions, connect the Thorin class and the class $M$, connect the class $M$ and the class of generalized type $G$ distributions. These classes are characterized by stochastic integral representations with respect to L{\'e}vy processes.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{delaPena:2009:EIS, author = "Victor de la Pe{\~n}a and Guodong Pang", title = "Exponential inequalities for self-normalized processes with applications", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "37:372--37:381", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1490", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1490", abstract = "We prove the following exponential inequality for a pair of random variables $ (A, B) $ with $ B > 0 $ satisfying the {\em canonical assumption\/}, $ E[\exp (\lambda A - \frac {\lambda^2}{2} B^2)] \leq 1 $ for $ \lambda \in R $, \par $$ P \left (\frac {|A|}{\sqrt { \frac {2q - 1}{q} \left (B^2 + (E[|A|^p])^{2 / p} \right) }} \geq x \right) \leq \left (\frac {q}{2q - 1} \right)^{\frac {q}{2q - 1}} x^{- \frac {q}{2q - 1}} e^{-x^2 / 2} $$ for $ x > 0 $, where $ 1 / p + 1 / q = 1 $ and $ p \geq 1 $. Applying this inequality, we obtain exponential bounds for the tail probabilities for self-normalized martingale difference sequences. We propose a method of hypothesis testing for the $ L^p$-norm $ (p \geq 1)$ of $A$ (in particular, martingales) and some stopping times. We apply this inequality to the stochastic TSP in $ [0, 1]^d$ ($ d \geq 2$), connected to the CLT.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "self-normalization, exponential inequalities, martingales, hypothesis testing, stochastic Traveling Salesman Problem", } @Article{Goncalves:2009:DFZ, author = "Patricia Goncalves and Milton Jara", title = "Density fluctuations for a zero-range process on the percolation cluster", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "38:382--38:395", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1491", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1491", abstract = "We prove that the density fluctuations for a zero-range process evolving on the $d$-dimensional supercritical percolation cluster, with $ d \geq {3}$, are given by a generalized Ornstein--Uhlenbeck process in the space of distributions $ \mathscr {S}'(\mathbb {R}^d)$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "percolation cluster, zero-range process, density fluctuations", } @Article{Nikeghbali:2009:BFR, author = "Ashkan Nikeghbali and Marc Yor", title = "The {Barnes} {$G$} function and its relations with sums and products of generalized {Gamma} convolution variables", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "39:396--39:411", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1488", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1488", abstract = "We give a probabilistic interpretation for the Barnes $G$-function which appears in random matrix theory and in analytic number theory in the important moments conjecture due to Keating-Snaith for the Riemann zeta function, via the analogy with the characteristic polynomial of random unitary matrices. We show that the Mellin transform of the characteristic polynomial of random unitary matrices and the Barnes $G$-function are intimately related with products and sums of gamma, beta and log-gamma variables. In particular, we show that the law of the modulus of the characteristic polynomial of random unitary matrices can be expressed with the help of products of gamma or beta variables. This leads us to prove some non standard type of limit theorems for the logarithmic mean of the so called generalized gamma convolutions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Barnes G-function, beta-gamma algebra, generalized gamma convolution variables, random matrices, characteristic polynomials of random unitary matrices", } @Article{Kargin:2009:SRT, author = "Vladislav Kargin", title = "Spectrum of random {Toeplitz} matrices with band structure", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "40:412--40:423", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1492", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1492", abstract = "This paper considers the eigenvalues of symmetric Toeplitz matrices with independent random entries and band structure. We assume that the entries of the matrices have zero mean and a uniformly bounded 4th moment, and we study the limit of the eigenvalue distribution when both the size of the matrix and the width of the band with non-zero entries grow to infinity. It is shown that if the bandwidth\slash size ratio converges to zero, then the limit of the eigenvalue distributions is Gaussian. If the ratio converges to a positive limit, then the distributions converge to a non-Gaussian distribution, which depends only on the limit ratio. A formula for the fourth moment of this distribution is derived.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "random matrices", } @Article{Schlemm:2009:FPP, author = "Eckhard Schlemm", title = "First-passage percolation on width-two stretches with exponential link weights", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "41:424--41:434", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1493", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1493", abstract = "We consider the first-passage percolation problem on effectively one-dimensional graphs with vertex set $ \{ 1, \dots, n \} \times \{ 0, 1 \} $ and translation-invariant edge-structure. For three of six non-trivial cases we obtain exact expressions for the asymptotic percolation rate $ \chi $ by solving certain recursive distributional equations and invoking results from ergodic theory to identify $ \chi $ as the expected asymptotic one-step growth of the first-passage time from $ (0, 0) $ to $ (n, 0) $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "First-passage percolation, percolation rate, Markov chains, ergodicity", } @Article{Fukushima:2009:LTQ, author = "Ryoki Fukushima", title = "From the {Lifshitz} tail to the quenched survival asymptotics in the trapping problem", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "42:435--42:446", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1497", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1497", abstract = "The survival problem for a diffusing particle moving among random traps is considered. We introduce a simple argument to derive the quenched asymptotics of the survival probability from the Lifshitz tail effect for the associated operator. In particular, the upper bound is proved in fairly general settings and is shown to be sharp in the case of the Brownian motion among Poissonian obstacles. As an application, we derive the quenched asymptotics for the Brownian motion among traps distributed according to a random perturbation of the lattice.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Lifshitz tail; random media; survival probability; Trapping problem", } @Article{Hoepfner:2009:EYW, author = "Reinhard Hoepfner", title = "An extension of the {Yamada--Watanabe} condition for pathwise uniqueness to stochastic differential equations with jumps", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "43:447--43:456", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1499", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1499", abstract = "We extend the Yamada--Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps, in the special case where small jumps are summable.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "SDE with jumps, pathwise uniqueness, Yamada--Watanabe condition", } @Article{Otobe:2009:TGD, author = "Yoshiki Otobe", title = "A type of {Gauss}' divergence formula on {Wiener} spaces", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "44:457--44:463", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1498", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1498", abstract = "We will formulate a type of Gauss' divergence formula on sets of functions which are greater than a specific value of which boundaries are not regular. Such formula was first established by L. Zambotti in 2002 with a profound study of stochastic processes. In this paper we will give a much shorter and simpler proof for his formula in a framework of the Malliavin calculus and give alternate expressions. Our approach also enables to show that such formulae hold in other Gaussian spaces.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "divergence formulae on the Wiener spaces, integration by parts formulae on the Wiener spaces", } @Article{Posfai:2009:EMC, author = "Anna Posfai", title = "An extension of {Mineka}'s coupling inequality", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "45:464--45:473", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1501", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1501", abstract = "In this paper we propose a refinement of Mineka's coupling inequality that gives a better upper bound for $ d_{TV} \left ({\cal L} \left (W \right), {\cal L} \left (W + 1 \right) \right) $, where $W$ is a sum of $n$ independent integer valued random variables, in the case when $ \text {Var} W \gg n$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "coupon collecting; Mineka coupling; total variation distance; translated compound Poisson approximation", } @Article{Goldstein:2009:BEB, author = "Larry Goldstein and Qi-Man Shao", title = "{Berry--Ess{\'e}en} Bounds for Projections of Coordinate Symmetric Random Vectors", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "46:474--46:485", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1502", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1502", abstract = "For a coordinate symmetric random vector $ (Y_1, \ldots, Y_n) = {\bf Y} \in \mathbb {R}^n $, that is, one satisfying $ (Y_1, \ldots, Y_n) =_d(e_1 Y_1, \ldots, e_n Y_n) $ for all $ (e_1, \ldots, e_n) \in \{ - 1, 1 \}^n $, for which $ P(Y_i = 0) = 0 $ for all $ i = 1, 2, \ldots, n $, the following Berry Ess{\'e}en bound to the cumulative standard normal $ \Phi $ for the standardized projection $ W_\theta = Y_\theta / v_\theta $ of $ {\bf Y} $ holds:\par $$ \sup_{x \in \mathbb {R}}|P(W_\theta \leq x) - \Phi (x)| \leq 2 \sum_{i = 1}^n | \theta_i|^3 E| X_i|^3 + 8.4 E(V_\theta^2 - 1)^2, $$ where $ Y_\theta = \theta \cdot {\bf Y} $ is the projection of $ {\bf Y} $ in direction $ \theta \in \mathbb {R}^n $ with $ || \theta || = 1 $, $ v_\theta = \sqrt {\mbox {Var}(Y_\theta)}, X_i = |Y_i| / v_\theta $ and $ V_\theta = \sum_{i = 1}^n \theta_i^2 X_i^2 $. As such coordinate symmetry arises in the study of projections of vectors chosen uniformly from the surface of convex bodies which have symmetries with respect to the coordinate planes, the main result is applied to a class of coordinate symmetric vectors which includes cone measure $ {\cal C}_p^n $ on the $ \ell_p^n $ sphere as a special case, resulting in a bound of order $ \sum_{i = 1}^n | \theta_i|^3 $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Borodin:2009:MDB, author = "Alexei Borodin and Patrik Ferrari and Michael Prahofer and Tomohiro Sasamoto and Jon Warren", title = "Maximum of {Dyson} {Brownian} motion and non-colliding systems with a boundary", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "47:486--47:494", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1503", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1503", abstract = "We prove an equality-in-law relating the maximum of GUE Dyson's Brownian motion and the non-colliding systems with a wall. This generalizes the well known relation between the maximum of a Brownian motion and a reflected Brownian motion", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Dyson Brownian motion, reflected Brownian motion, non-colliding systems with a wall", } @Article{Chatterjee:2009:OAS, author = "Sourav Chatterjee and Michel Ledoux", title = "An observation about submatrices", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "48:495--48:500", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1504", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1504", abstract = "Let $M$ be an arbitrary Hermitian matrix of order $n$, and $k$ be a positive integer less than $n$. We show that if $k$ is large, the distribution of eigenvalues on the real line is almost the same for almost all principal submatrices of $M$ of order $k$. The proof uses results about random walks on symmetric groups and concentration of measure. In a similar way, we also show that almost all $ k \times n$ submatrices of $M$ have almost the same distribution of singular values.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random matrix, concentration of measure, empirical distribution, eigenvalue", } @Article{Ruggiero:2009:CRI, author = "Matteo Ruggiero and Stephen Walker", title = "Countable representation for infinite dimensional diffusions derived from the two-parameter {Poisson--Dirichlet} process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "49:501--49:517", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1508", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1508", abstract = "This paper provides a countable representation for a class of infinite-dimensional diffusions which extends the infinitely-many-neutral-alleles model and is related to the two-parameter Poisson--Dirichlet process. By means of Gibbs sampling procedures, we define a reversible Moran-type population process. The associated process of ranked relative frequencies of types is shown to converge in distribution to the two-parameter family of diffusions, which is stationary and ergodic with respect to the two-parameter Poisson--Dirichlet distribution. The construction provides interpretation for the limiting process in terms of individual dynamics.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Gibbs sampler; infinite-dimensional diffusion; population process; stationary distribution; Two-parameter Poisson--Dirichlet process", } @Article{Hu:2009:NDP, author = "Yueyun Hu and Qi-Man Shao", title = "A note on directed polymers in {Gaussian} environments", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "50:518--50:528", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1509", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1509", abstract = "We study the problem of directed polymers in Gaussian environments in $ \mathbb {Z}^d $ from the viewpoint of a Gaussian family indexed by the set of random walk paths. In the zero-temperature case, we give a numerical bound on the maximum of the Hamiltonian, whereas in the finite temperature case, we establish an equivalence between the {"very} strong {disorder"} and the growth rate of the entropy associated to the model", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Directed polymer, Gaussian environment", } @Article{Hu:2009:SIR, author = "Yaozhong Hu and David Nualart", title = "Stochastic integral representation of the {$ L^2 $} modulus of {Brownian} local time and a central limit theorem", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "51:529--51:539", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1511", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1511", abstract = "The purpose of this note is to prove a central limit theorem for the $ L^2$-modulus of continuity of the Brownian local time obtained in [3], using techniques of stochastic analysis. The main ingredients of the proof are an asymptotic version of Knight's theorem and the Clark-Ocone formula for the $ L^2$-modulus of the Brownian local time", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Malliavin calculus, Clark-Ocone formula, Brownian local time, Knight theorem, central limit theorem, Tanaka formula", } @Article{Liu:2009:IRF, author = "Wei Liu and Liming Wu", title = "Identification of the rate function for large deviations of an irreducible {Markov} chain", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "52:540--52:551", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1512", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1512", abstract = "For an irreducible Markov chain $ (X_n)_{n \ge 0} $ we identify the rate function governing the large deviation estimation of empirical mean $ \frac {1}{n} \sum_{k = 0}^{n - 1} f(X_k) $ by means of the Donsker-Varadhan's entropy. That allows us to obtain the lower bound of large deviations for the empirical measure $ \frac {1}{n} \sum_{k = 0}^{n - 1} \delta_{X_k} $ in full generality", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Large deviations, irreducible Markov processes, Feynman--Kac semigroups", } @Article{Jegaraj:2009:STA, author = "Terence Jegaraj", title = "Small time asymptotics of {Ornstein--Uhlenbeck} densities in {Hilbert} spaces", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "53:552--53:559", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1510", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1510", abstract = "We show that Varadhan's small time asymptotics for densities of the solution of a stochastic differential equation in $ \mathbb {R}^n $ carries over to a Hilbert space-valued Ornstein--Uhlenbeck process whose transition semigroup is strongly Feller and symmetric. In the Hilbert space setting, densities are with respect to a Gaussian invariant measure.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "small time asymptotics, densities, Ornstein--Uhlenbeck, Hilbert space", } @Article{Es-Sarhir:2009:HIF, author = "Abdelhadi Es-Sarhir and Max-K. von Renesse and Michael Scheutzow", title = "{Harnack} Inequality for Functional {SDEs} with Bounded Memory", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "54:560--54:565", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1513", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1513", abstract = "We use a coupling method for functional stochastic differential equations with bounded memory to establish an analogue of Wang's dimension-free Harnack inequality \url{http://www.springerlink.com/content/8wllev0xwbe3kvkc/}. The strong Feller property for the corresponding segment process is also obtained.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Harnack Inequality, Coupling, Strong Feller Property", } @Article{Lalley:2009:GIH, author = "Steven Lalley and Gregory Lawler and Hariharan Narayanan", title = "Geometric Interpretation of Half-Plane Capacity", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "55:566--55:571", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1517", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1517", abstract = "Schramm-Loewner Evolution describes the scaling limits of interfaces in certain statistical mechanical systems. These interfaces are geometric objects that are not equipped with a canonical parametrization. The standard parametrization of SLE is via half-plane capacity, which is a conformal measure of the size of a set in the reference upper half-plane. This has useful harmonic and complex analytic properties and makes SLE a time-homogeneous Markov process on conformal maps. In this note, we show that the half-plane capacity of a hull $A$ is comparable up to multiplicative constants to more geometric quantities, namely the area of the union of all balls centered in $A$ tangent to $R$, and the (Euclidean) area of a $1$-neighborhood of $A$ with respect to the hyperbolic metric.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion, Schramm-Loewner Evolution", } @Article{Eichelsbacher:2009:MDT, author = "Peter Eichelsbacher and Jens Sommerauer", title = "Moderate deviations for traces of words in a mult-matrix model", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "56:572--56:586", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1515", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1515", abstract = "We prove a moderate deviation principle for traces of words of weakly interacting random matrices defined by a multi-matrix model with a potential being a small perturbation of the GUE. The remarkable strength of high order expansions of the matrix model recently found by Guionnet and Maurel-Segala is the key fact that allows us to develop our result and provides also an alternative proof for a special case of the central limit theorem for traces of words, studied in the article of Guionnet and Maurel-Segala (2006).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random matrices, moderate deviations, map enumeration", } @Article{Kulske:2009:SEB, author = "Christof K{\"u}lske and Marco Formentin", title = "A symmetric entropy bound on the non-reconstruction regime of {Markov} chains on {Galton--Watson} trees", journal = j-ELECTRON-COMMUN-PROBAB, volume = "14", pages = "57:587--57:596", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v14-1516", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1516", abstract = "We give a criterion for the non-reconstructability of tree-indexed $q$-state Markov chains obtained by broadcasting a signal from the root with a given transition matrix $M$. Non-reconstruction holds if $ c(M)$ times the expected number of offspring on the Galton--Watson tree is smaller than 1. Here $ c(M)$ is an explicit function, which is convex over the set of $M$'s with a given invariant distribution, that is defined in terms of a $ (q - 1)$-dimensional variational problem over symmetric entropies. This result is equivalent to proving the extremality of the free boundary condition Gibbs measure within the corresponding Gibbs-simplex. Our theorem holds for possibly non-reversible $M$ and its proof is based on a general recursion formula for expectations of a symmetrized relative entropy function, which invites their use as a Lyapunov function. In the case of the Potts model, the present theorem reproduces earlier results of the authors, with a simplified proof, in the case of the symmetric Ising model (where the argument becomes similar to the approach of Pemantle and Peres) the method produces the correct reconstruction threshold), in the case of the (strongly) asymmetric Ising model where the Kesten-Stigum bound is known to be not sharp the method provides improved numerical bounds.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Broadcasting on trees, Gibbs measures, random tree, Galton--Watson tree, reconstruction problem, free boundary condition", } @Article{Georgiou:2010:SER, author = "Nicos Georgiou", title = "Soft edge results for longest increasing paths on the planar lattice", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "1:1--1:13", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1519", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1519", abstract = "For two-dimensional last-passage time models of weakly increasing paths, interesting scaling limits have been proved for points close the axis (the hard edge). For strictly increasing paths of Bernoulli($p$) marked sites, the relevant boundary is the line $ y = p x$. We call this the soft edge to contrast it with the hard edge. We prove laws of large numbers for the maximal cardinality of a strictly increasing path in the rectangle $ [p^{-1}n - x n^a] \times [n]$ as the parameters $a$ and $x$ vary. The results change qualitatively as $a$ passes through the value $ 1 / 2$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Bernoulli matching model; Discrete TASEP; increasing paths; last passage model; soft edge; weak law of large numbers", } @Article{Dirr:2010:LP, author = "Nicolas Dirr and Patrick Dondl and Geoffrey Grimmett and Alexander Holroyd and Michael Scheutzow", title = "{Lipschitz} percolation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "2:14--2:21", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1521", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1521", abstract = "We prove the existence of a (random) Lipschitz function $ F : \mathbb {Z}^{d - 1} \to \mathbb {Z}^+ $ such that, for every $ x \in \mathbb {Z}^{d - 1} $, the site $ (x, F(x)) $ is open in a site percolation process on $ \mathbb {Z}^d $. The Lipschitz constant may be taken to be $1$ when the parameter $p$ of the percolation model is sufficiently close to $1$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "percolation, Lipschitz embedding, random surface", } @Article{Zhou:2010:ASF, author = "Xiaowen Zhou", title = "Almost sure finiteness for the total occupation time of an $ (d, \alpha, \beta)$-superprocess", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "3:22--3:31", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1523", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1523", abstract = "For $ 0 < \alpha \leq 2 $ and $ 0 < \beta \leq 1 $ let $X$ be the $ (d, \alpha, \beta)$-superprocess, i.e. the superprocess with $ \alpha $-stable spatial movement in $ R^d$ and $ (1 + \beta)$-stable branching. Given that the initial measure $ X_0$ is Lebesgue on $ R^d$, Iscoe conjectured in [7] that the total occupational time $ \int_0^\infty X_t(B)d t$ is a.s. finite if and only if $ d \beta < \alpha $, where $B$ denotes any bounded Borel set in $ R^d$ with non-empty interior.\par In this note we give a partial answer to Iscoe's conjecture by showing that $ \int_0^\infty X_t(B)d t < \infty $ a.s. if $ 2 d \beta < \alpha $ and, on the other hand, $ \int_0^\infty X_t(B)d t = \infty $ a.s. if $ d \beta > \alpha $.\par For $ 2 d \beta < \alpha $, our result can also imply the a.s. finiteness of the total occupation time (over any bounded Borel set) and the a.s. local extinction for the empirical measure process of the $ (d, \alpha, \beta)$-branching particle system with Lebesgue initial intensity measure.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Takeda:2010:FKP, author = "Masayoshi Takeda", title = "{Feynman--Kac} Penalisations of Symmetric Stable Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "4:32--4:43", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1524", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1524", abstract = "In K. Yano, Y. Yano and M. Yor (2009), limit theorems for the one-dimensional symmetric $ \alpha $-stable process normalized by negative (killing) Feynman--Kac functionals were studied. We consider the same problem and extend their results to positive Feynman--Kac functionals of multi-dimensional symmetric $ \alpha $-stable processes.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Feynman--Kac functional; Kato measure; penalisation; symmetric stable process", } @Article{Beffara:2010:SLP, author = "Vincent Beffara and Sacha Friedli and Yvan Velenik", title = "Scaling Limit of the Prudent Walk", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "5:44--5:58", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1527", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1527", abstract = "We describe the scaling limit of the nearest neighbour prudent walk on $ Z^2 $, which performs steps uniformly in directions in which it does not see sites already visited. We show that the scaling limit is given by the process $ Z_u = \int_0^{3u / 7} (\sigma_1 1_{W(s) \geq 0} \vec {e}_1 + \sigma_2 1_{W(s) \geq 0} \vec {e}_2) d s $, $ u \in [0, 1] $, where $W$ is the one-dimensional Brownian motion and $ \sigma_1, \sigma_2$ two random signs. In particular, the asymptotic speed of the walk is well-defined in the $ L^1$-norm and equals 3/7.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "prudent self-avoiding walk, brownian motion, scaling limit, ballistic behaviour, ageing", } @Article{Kovchegov:2010:OPM, author = "Yevgeniy Kovchegov", title = "Orthogonality and probability: mixing times", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "6:59--6:67", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1525", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1525", abstract = "We produce the first example of bounding total variation distance to stationarity and estimating mixing times via orthogonal polynomials diagonalization of discrete reversible Markov chains, the Karlin-McGregor approach.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "orthogonal polynomials, random walks, mixing rates", } @Article{Nagahata:2010:NDS, author = "Yukio Nagahata and Nobuo Yoshida", title = "A Note on the Diffusive Scaling Limit for a Class of Linear Systems", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "7:68--7:78", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1530", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1530", abstract = "We consider a class of continuous-time stochastic growth models on $d$-dimensional lattice with non-negative real numbers as possible values per site. We remark that the diffusive scaling limit proven in our previous work [NY09a] can be extended to wider class of models so that it covers the cases of potlatch/smoothing processes.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "diffusive scaling limit, linear systems, binary contact process, potlatch process, smoothing process", } @Article{Gnedin:2010:SSM, author = "Alexander Gnedin", title = "A Species Sampling Model with Finitely Many Types", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "8:79--8:88", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1532", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1532", abstract = "A two-parameter family of exchangeable partitions with a simple updating rule is introduced. The partition is identified with a randomized version of a standard symmetric Dirichlet species-sampling model with finitely many types. A power-like distribution for the number of types is derived.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "exchangeability, Gibbs partition, succession rule", } @Article{Samee:2010:PSF, author = "Farman Samee", title = "On the Principle of Smooth Fit for Killed Diffusions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "9:89--9:98", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1531", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1531", abstract = "We explore the principle of smooth fit in the case of the discounted optimal stopping problem\par $$ V(x) = \sup_\tau \, \mathsf {E}_x[e^{- \beta \tau }G(X_\tau)]. $$ We show that there exists a regular diffusion $X$ and differentiable gain function $G$ such that the value function $V$ above fails to satisfy the smooth fit condition $ V'(b) = G'(b)$ at the optimal stopping point $b$. However, if the fundamental solutions $ \psi $ and $ \phi $ of the `killed' generator equation $ L_X u(x) - \beta u(x) = 0$ are differentiable at $b$ then the smooth fit condition $ V'(b) = G'(b)$ holds (whenever $X$ is regular and $G$ is differentiable at $b$). We give an example showing that this can happen even when `smooth fit through scale' (in the sense of the discounted problem) fails.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "concave function; discounted optimal stopping; killed diffusion process; Optimal stopping; principle of smooth fit; regular diffusion process; scale function", } @Article{Bass:2010:MHT, author = "Richard Bass", title = "The measurability of hitting times", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "10:99--10:105", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1535", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", note = "See correction \cite{Bass:2011:CMH}.", URL = "http://ecp.ejpecp.org/article/view/1535", abstract = "Under very general conditions the hitting time of a set by a stochastic process is a stopping time. We give a new simple proof of this fact. The section theorems for optional and predictable sets are easy corollaries of the proof.\par A correction to this paper has been published : \url{http://www.math.washington.edu/~ejpecp/ECP/viewarticle.php?id=2291&layout=abstract} Electronic Communications in Probability, Vol. 16 (2011), paper 18.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stopping time, hitting time, progressively measurable, optional, predictable, debut theorem, section theorem", } @Article{Fang:2010:CMD, author = "Ming Fang and Ofer Zeitouni", title = "Consistent Minimal Displacement of Branching Random Walks", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "11:106--11:118", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1533", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1533", abstract = "Let $ \mathbb {T} $ denote a rooted $b$-ary tree and let $ \{ S_v \}_{v \in \mathbb {T}}$ denote a branching random walk indexed by the vertices of the tree, where the increments are i.i.d. and possess a logarithmic moment generating function $ \Lambda (\cdot)$. Let $ m_n$ denote the minimum of the variables $ S_v$ over all vertices at the $n$ th generation, denoted by $ \mathbb {D}_n$. Under mild conditions, $ m_n / n$ converges almost surely to a constant, which for convenience may be taken to be $0$. With $ \bar S_v = \max \{ S_w : w$ is on the geodesic connecting the root to $ v \} $, define $ L_n = \min_{v \in \mathbb {D}_n} \bar S_v$. We prove that $ L_n / n^{1 / 3}$ converges almost surely to an explicit constant $ l_0$. This answers a question of Hu and Shi.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Branching Random Walk; Consistent Minimal Displacement", } @Article{Gurel-Gurevich:2010:FAR, author = "Ori Gurel-Gurevich and Gideon Amir", title = "On Fixation of Activated Random Walks", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "12:119--12:123", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1536", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1536", abstract = "We prove that for the Activated Random Walks model on transitive unimodular graphs, if there is fixation, then every particle eventually fixates, almost surely. We deduce that the critical density is at most 1. Our methods apply for much more general processes on unimodular graphs. Roughly put, our result apply whenever the path of each particle has an automorphism invariant distribution and is independent of other particles' paths, and the interaction between particles is automorphism invariant and local. In particular, we do not require the particles path distribution to be Markovian. This allows us to answer a question of Rolla and Sidoravicius, in a more general setting then had been previously known (by Shellef).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Activated Random Walks; Interacting Particles System", } @Article{Fontbona:2010:MOT, author = "Joaquin Fontbona and H{\'e}l{\`e}ne Gu{\'e}rin and Sylvie M{\'e}l{\'e}ard", title = "Measurability of optimal transportation and strong coupling of martingale measures", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "13:124--13:133", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1534", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1534", abstract = "We consider the optimal mass transportation problem in $ \mathbb {R}^d $ with measurably parameterized marginals under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability result for this map, with respect to the space variable and to the parameter. The proof needs to establish the measurability of some set-valued mappings, related to the support of the optimal transference plans, which we use to perform a suitable discrete approximation procedure. A motivation is the construction of a strong coupling between orthogonal martingale measures. By this we mean that, given a martingale measure, we construct in the same probability space a second one with a specified covariance measure process. This is done by pushing forward the first martingale measure through a predictable version of the optimal transport map between the covariance measures. This coupling allows us to obtain quantitative estimates in terms of the Wasserstein distance between those covariance measures.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Measurability of optimal transport. Coupling between orthogonal martingale measures. Predictable transport process.", } @Article{Basak:2010:BRT, author = "Aniran Basak and Arup Bose", title = "Balanced random and {Toeplitz} matrices", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "14:134--14:148", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1537", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1537", abstract = "Except for the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist share a common property --- the number of times each random variable appears in the matrix is (more or less) the same across the variables. Thus it seems natural to ask what happens to the spectrum of the Toeplitz and Hankel matrices when each entry is scaled by the square root of the number of times that entry appears in the matrix instead of the uniform scaling by $ n^{-1 / 2} $. We show that the LSD of these balanced matrices exist and derive integral formulae for the moments of the limit distribution. Curiously, it is not clear if these moments define a unique distribution", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random matrix, eigenvalues, balanced matrix, moment method, bounded Lipschitz metric, Carleman condition, almost sure convergence, convergence in distribution, uniform integrability.", } @Article{Ignatiouk-Robert:2010:MBR, author = "Irina Ignatiouk-Robert", title = "{$T$}-{Martin} boundary of reflected random walks on a half-space", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "15:149--15:161", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1541", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1541", abstract = "The $t$-Martin boundary of a random walk on a half-space with reflected boundary conditions is identified. It is shown in particular that the $t$-Martin boundary of such a random walk is not stable in the following sense: for different values of $t$, the $t$-Martin compactifications are not equivalent.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "t-Martin boundary, Markov chain, stability", } @Article{Petrov:2010:RSP, author = "Leonid Petrov", title = "Random Strict Partitions and Determinantal Point Processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "16:162--16:175", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1542", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1542", abstract = "We present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice $ \{ 1, 2, \dots \} $ or on the open half-line $ (0, + \infty) $. The main result is the computation of the correlation kernels. They have integrable form and are expressed through the Euler gamma function (the lattice case) and the classical Whittaker functions (the continuous case). Our processes are obtained via a limit transition from a model of random strict partitions introduced by Borodin (1997) in connection with the problem of harmonic analysis for projective characters of the infinite symmetric group.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "determinantal point process; Macdonald kernel; random strict partitions", } @Article{Raschel:2010:GFM, author = "Kilian Raschel", title = "{Green} functions and {Martin} compactification for killed random walks related to {$ {\rm SU}(3) $}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "17:176--17:190", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1543", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1543", abstract = "We consider the random walks killed at the boundary of the quarter plane, with homogeneous non-zero jump probabilities to the eight nearest neighbors and drift zero in the interior, and which admit a positive harmonic polynomial of degree three. For these processes, we find the asymptotic of the Green functions along all infinite paths of states, and from this we deduce that the Martin compactification is the one-point compactification.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "killed random walks, Green functions, Martin compactification, uniformization.", } @Article{Bojdecki:2010:PSQ, author = "Tomasz Bojdecki and Luis Gorostiza and Anna Talarczyk", title = "Particle systems with quasi-homogeneous initial states and their occupation time fluctuations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "18:191--18:202", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1547", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1547", abstract = "We consider particle systems in $R$ with initial configurations belonging to a class of measures that obey a quasi-homogeneity property, which includes as special cases homogeneous Poisson measures and many deterministic measures (simple example: one atom at each point of $Z$). The particles move independently according to an alpha-stable L{\'e}vy process, $ \alpha > 1$, and we also consider the model where they undergo critical branching. Occupation time fluctuation limits of such systems have been studied in the Poisson case. For the branching system in ``low'' dimension the limit was characterized by a process called sub-fractional Brownian motion, and this process was attributed to the branching because it had appeared only in that case. In the present more general framework sub-fractional Brownian motion is more prevalent, namely, it also appears as a component of the limit for the system without branching in ``low'' dimension. A new method of proof, based on the central limit theorem, is used.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "branching; distribution-valued process; limit theorem; occupation time fluctuation; particle system; stable process; sub-fractional Brownian motion", } @Article{Oliveira:2010:SRH, author = "Roberto Oliveira", title = "Sums of random {Hermitian} matrices and an inequality by {Rudelson}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "19:203--19:212", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1544", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1544", abstract = "We give a new, elementary proof of a key inequality used by Rudelson in the derivation of his well-known bound for random sums of rank-one operators. Our approach is based on Ahlswede and Winter's technique for proving operator Chernoff bounds. We also prove a concentration inequality for sums of random matrices of rank one with explicit constants.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "concentration inequalities; Khintchine inequalities.; Random Hermitian matrices", } @Article{Attanasio:2010:SFD, author = "Stefano Attanasio", title = "Stochastic flows of diffeomorphisms for one-dimensional {SDE} with discontinuous drift", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "20:213--20:226", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1545", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1545", abstract = "The existence of a stochastic flow of class $ C^{1, \alpha } $, for $ \alpha < 1 / 2 $, for a 1-dimensional SDE will be proved under mild conditions on the regularity of the drift. The diffusion coefficient is assumed constant for simplicity, while the drift is an autonomous BV function with distributional derivative bounded from above or from below. To reach this result the continuity of the local time with respect to the initial datum will also be proved.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stochastic flows, Local time", } @Article{Maejima:2010:CMI, author = "Makoto Maejima and Yohei Ueda", title = "Compositions of mappings of infinitely divisible distributions with applications to finding the limits of some nested subclasses", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "21:227--21:239", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1557", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1557", abstract = "Let $ \{ X_t^{(\mu)}, t \ge 0 \} $ be a L{\'e}vy process on $ R^d $ whose distribution at time 1 is $ \mu $, and let $f$ be a nonrandom measurable function on $ (0, a), 0 < a \leq \infty $. Then we can define a mapping $ \Phi_f(\mu)$ by the law of $ \int_0^a f(t)d X_t^{(\mu)}$, from $ \mathfrak D(\Phi_f)$ which is the totality of $ \mu \in I(R^d)$ such that the stochastic integral $ \int_0^a f(t)d X_t^{(\mu)}$ is definable, into a class of infinitely divisible distributions. For $ m \in N$, let $ \Phi_f^m$ be the $m$ times composition of $ \Phi_f$ itself. Maejima and Sato (2009) proved that the limits $ \bigcap_{m = 1}^\infty \Phi^m_f(\mathfrak D(\Phi^m_f))$ are the same for several known $f$'s. Maejima and Nakahara (2009) introduced more general $f$'s. In this paper, the limits $ \bigcap_{m = 1}^\infty \Phi^m_f(\mathfrak D(\Phi^m_f))$ for such general $f$'s are investigated by using the idea of compositions of suitable mappings of infinitely divisible distributions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "infinitely divisible distribution on $\{\mathbb R\}^d$, stochastic integral mapping, composition of mappings, limit of nested subclasses", } @Article{Vandenberg-Rodes:2010:LTP, author = "Alexander Vandenberg-Rodes", title = "A limit theorem for particle current in the symmetric exclusion process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "22:240--22:252", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1550", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1550", abstract = "Using the recently discovered strong negative dependence properties of the symmetric exclusion process, we derive general conditions for when the normalized current of particles between regions converges to the Gaussian distribution. The main novelty is that the results do not assume any translation invariance, and hold for most initial configurations.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "central limit theorem; particle current; stability; symmetric exclusion process", } @Article{Bertoin:2010:TTS, author = "Jean Bertoin", title = "A two-time-scale phenomenon in a fragmentation-coagulation process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "23:253--23:262", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1552", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1552", abstract = "Consider two urns, $A$ and $B$, where initially $A$ contains a large number $n$ of balls and $B$ is empty. At each step, with equal probability, either we pick a ball at random in $A$ and place it in $B$, or vice-versa (provided of course that $A$, or $B$, is not empty). The number of balls in $B$ after $n$ steps is of order $ \sqrt n$, and this number remains essentially the same after $ \sqrt n$ further steps. Observe that each ball in the urn $B$ after $n$ steps has a probability bounded away from $0$ and $1$ to be placed back in the urn $A$ after $ \sqrt n$ additional steps. So, even though the number of balls in $B$ does not evolve significantly between $n$ and $ n + \sqrt n$, the precise contain of urn $B$ does.\par This elementary observation is the source of an interesting two-time-scale phenomenon which we illustrate using a simple model of fragmentation-coagulation. Inspired by Pitman's construction of coalescing random forests, we consider for every $ n \in \mathbb {N}$ a uniform random tree with $n$ vertices, and at each step, depending on the outcome of an independent fair coin tossing, either we remove one edge chosen uniformly at random amongst the remaining edges, or we replace one edge chosen uniformly at random amongst the edges which have been removed previously. The process that records the sizes of the tree-components evolves by fragmentation and coagulation. It exhibits subaging in the sense that when it is observed after $k$ steps in the regime $ k \sim t n + s \sqrt n$ with $ t > 0$ fixed, it seems to reach a statistical equilibrium as $ n \to \infty $; but different values of $t$ yield distinct pseudo-stationary distributions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Two-time-scale, fragmentation, coagulation, random forest, subaging.", } @Article{Doring:2010:ART, author = "Leif D{\"o}ring and Mladen Savov", title = "An Application of Renewal Theorems to Exponential Moments of Local Times", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "24:263--24:269", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1558", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1558", abstract = "In this note we explain two transitions known for moment generating functions of local times by means of properties of the renewal measure of a related renewal equation. The arguments simplify and strengthen results on the asymptotic behavior in the literature", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Renewal Theorem, Local Times", } @Article{Cattiaux:2010:PIC, author = "Patrick Cattiaux and Arnaud Guillin and Cyril Roberto", title = "Poincar{\'e} inequality and the {$ L^p $} convergence of semi-groups", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "25:270--25:280", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1559", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1559", abstract = "We prove that for symmetric Markov processes of diffusion type admitting a ``carr{\'e} du champ'', the Poincar{\'e} inequality is equivalent to the exponential convergence of the associated semi-group in one (resp. all) $ L^p(\mu) $ spaces for $ 1 < p < \infty $. We also give the optimal rate of convergence. Part of these results extends to the stationary, not necessarily symmetric situation.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Poincar{\'e} inequality, rate of convergence", } @Article{Borovkov:2010:DBM, author = "Konstantin Borovkov", title = "On the distribution of the {Brownian} motion process on its way to hitting zero", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "26:281--26:285", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1555", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1555", abstract = "We present functional versions of recent results on the univariate distributions of the process $ V_{x, u} = x + W_{u \tau (x)}, $ $ 0 \le u \le 1 $, where $ W_\bullet $ is the standard Brownian motion process, $ x > 0 $ and $ \tau (x) = \inf \{ t > 0 : \, W_t = - x \} $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Bessel bridge; Brownian meander; Brownian motion; hitting time", } @Article{Konig:2010:RWC, author = "Wolfgang K{\"o}nig and Patrick Schmid", title = "Random walks conditioned to stay in {Weyl} chambers of type {C} and {D}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "27:286--27:296", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1560", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1560", abstract = "We construct the conditional versions of a multidimensional random walk given that it does not leave the Weyl chambers of type C and of type D, respectively, in terms of a Doob $h$-transform. Furthermore, we prove functional limit theorems for the rescaled random walks. This is an extension of recent work by Eichelsbacher and Koenig who studied the analogous conditioning for the Weyl chamber of type A. Our proof follows recent work by Denisov and Wachtel who used martingale properties and a strong approximation of random walks by Brownian motion. Therefore, we are able to keep minimal moment assumptions. Finally, we present an alternate function that is amenable to an $h$-transform in the Weyl chamber of type C.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Conditional random walks, Doob $h$-transform, non-colliding probability, harmonic functions, r{\'e}duite, Weyl chamber", } @Article{Sapozhnikov:2010:UBE, author = "Artem Sapozhnikov", title = "Upper bound on the expected size of the intrinsic ball", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "28:297--28:298", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1553", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1553", abstract = "We give a short proof of Theorem 1.2 (i) from the paper {"The} Alexander-Orbach conjecture holds in high {dimensions"} by G. Kozma and A. Nachmias. We show that the expected size of the intrinsic ball of radius $r$ is at most $ C r$ if the susceptibility exponent is at most 1. In particular, this result follows if the so-called triangle condition holds.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "chemical distance; Critical percolation; high-dimensional percolation; intrinsic ball; triangle condition", } @Article{Bose:2010:SNC, author = "Arup Bose and Rajat Hazra and Koushik Saha", title = "Spectral norm of circulant type matrices with heavy tailed entries", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "29:299--29:313", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1554", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1554", abstract = "We first study the probabilistic properties of the spectral norm of scaled eigenvalues of large dimensional Toeplitz, circulant and symmetric circulant matrices when the input sequence is independent and identically distributed with appropriate heavy tails. When the input sequence is a stationary two sided moving average process of infinite order, we scale the eigenvalues by the spectral density at appropriate ordinates and study the limit for their maximums.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "circulant matrix; eigenvalues; Large dimensional random matrix; moving average process; power transfer function; reverse circulant matrix; spectral norm; symmetric circulant matrix; Toeplitz matrix", } @Article{Bardina:2010:WAF, author = "Xavier Bardina and Carles Rovira and Samy Tindel", title = "Weak approximation of fractional {SDEs}: the {Donsker} setting", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "30:314--30:329", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1561", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1561", abstract = "In this note, we take up the study of weak convergence for stochastic differential equations driven by a (Liouville) fractional Brownian motion $B$ with Hurst parameter $ H \in (1 / 3, 1 / 2)$, initiated in a paper of Bardina et al. (2010, \url{http://www.ams.org/mathscinet-getitem?mr=MR2565851} {\bf MR2565851}). In the current paper, we approximate the $d$-dimensional fBm by the convolution of a rescaled random walk with Liouville's kernel. We then show that the corresponding differential equation converges in law to a fractional SDE driven by $B$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Weak approximation, Kac-Stroock type approximation, fractional Brownian motion, rough paths", } @Article{Panchenko:2010:DSR, author = "Dmitry Panchenko", title = "On the {Dovbysh--Sudakov} representation result", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "31:330--31:338", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1562", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1562", abstract = "We present a detailed proof of the Dovbysh--Sudakov representation for symmetric positive definite weakly exchangeable infinite random arrays, called Gram-de Finetti matrices, which is based on the representation result of Aldous and Hoover for arbitrary (not necessarily positive definite) symmetric weakly exchangeable arrays.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "exchangeability, spin glasses.", } @Article{Albin:2010:NPO, author = "J. M. P. Albin and Hyemi Choi", title = "A new proof of an old result by {Pickands}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "32:339--32:345", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1566", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1566", abstract = "Let $ \{ \xi (t) \}_{t \in [0, h]} $ be a stationary Gaussian process with covariance function $r$ such that $ r(t) = 1 - C|t|^{\alpha } + o(|t|^{\alpha })$ as $ t \to 0$. We give a new and direct proof of a result originally obtained by Pickands, on the asymptotic behaviour as $ u \to \infty $ of the probability $ \Pr \{ \sup_{t \in [0, h]} \xi (t) > u \} $ that the process $ \xi $ exceeds the level $u$. As a by-product, we obtain a new expression for Pickands constant $ H_\alpha $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "extremes; Pickands constant; Stationary Gaussian process", } @Article{Chakrabarty:2010:CLT, author = "Arijit Chakrabarty", title = "{Central Limit Theorem} for truncated heavy tailed {Banach} valued random vectors", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "33:346--33:364", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1564", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1564", abstract = "In this paper the question of the extent to which truncated heavy tailed random vectors, taking values in a Banach space, retain the characteristic features of heavy tailed random vectors, is answered from the point of view of the central limit theorem.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "heavy tails, truncation, regular variation, central limit theorem, probability on Banach spaces", } @Article{Iksanov:2010:EMF, author = "Alexander Iksanov and Matthias Meiners", title = "Exponential Moments of First Passage Times and Related Quantities for Random Walks", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "34:365--34:375", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1569", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1569", abstract = "For a zero-delayed random walk on the real line, let $ \tau (x) $, $ N(x) $ and $ \rho (x) $ denote the first passage time into the interval $ (x, \infty) $, the number of visits to the interval $ ( - \infty, x] $ and the last exit time from $ ( - \infty, x] $, respectively. In the present paper, we provide ultimate criteria for the finiteness of exponential moments of these quantities. Moreover, whenever these moments are finite, we derive their asymptotic behaviour, as $ x \to \infty $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "first-passage time, last exit time, number of visits, random walk, renewal theory", } @Article{Bianchi:2010:AIS, author = "Pascal Bianchi and M{\'e}rouane Debbah and Jamal Najim", title = "Asymptotic Independence in the Spectrum of the {Gaussian} Unitary Ensemble", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "35:376--35:395", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1568", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1568", abstract = "Consider a $ n \times n $ matrix from the Gaussian Unitary Ensemble (GUE). Given a finite collection of bounded disjoint real Borel sets $ (\Delta_{i, n}, \ 1 \leq i \leq p) $ with positive distance from one another, eventually included in any neighbourhood of the support of Wigner's semi-circle law and properly rescaled (with respective lengths $ n^{-1} $ in the bulk and $ n^{-2 / 3} $ around the edges), we prove that the related counting measures $ {\mathcal N}_n(\Delta_{i, n}), (1 \leq i \leq p) $, where $ {\mathcal N}_n(\Delta) $ represents the number of eigenvalues within $ \Delta $, are asymptotically independent as the size $n$ goes to infinity, $p$ being fixed. As a consequence, we prove that the largest and smallest eigenvalues, properly centered and rescaled, are asymptotically independent; we finally describe the fluctuations of the ratio of the extreme eigenvalues of a matrix from the GUE.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "asymptotic independence; eigenvalues; Gaussian unitary ensemble; Random matrix", } @Article{Hu:2010:CLT, author = "Yaozhong Hu and David Nualart", title = "Central limit theorem for the third moment in space of the {Brownian} local time increments", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "36:396--36:410", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1573", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1573", abstract = "The purpose of this note is to prove a central limit theorem for the third integrated moment of the Brownian local time increments using techniques of stochastic analysis. The main ingredients of the proof are an asymptotic version of Knight's theorem and the Clark-Ocone formula for the third integrated moment of the Brownian local time increments.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion, local time, Clark-Ocone formula", } @Article{Unterberger:2010:MES, author = "Jeremie Unterberger", title = "Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional {Brownian} motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "37:411--37:417", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1574", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1574", abstract = "As a general rule, differential equations driven by a multi-dimensional irregular path $ \Gamma $ are solved by constructing a rough path over $ \Gamma $. The domain of definition - and also estimates - of the solutions depend on upper bounds for the rough path; these general, deterministic estimates are too crude to apply e.g. to the solutions of stochastic differential equations with linear coefficients driven by a Gaussian process with Holder regularity $ \alpha < 1 / 2 $. We prove here (by showing convergence of Chen's series) that linear stochastic differential equations driven by analytic fractional Brownian motion [6, 7] with arbitrary Hurst index $ \alpha \in (0, 1) $ may be solved on the closed upper half-plane, and that the solutions have finite variance.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "H{\"o}lder continuity, Chen series; stochastic differential equations, fractional Brownian motion, analytic fractional Brownian motion, rough paths", } @Article{Lacoin:2010:MAD, author = "Hubert Lacoin", title = "The Martingale approach to disorder irrelevance for pinning models", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "38:418--38:427", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1572", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1572", abstract = "This paper presents a very simple and self-contained proof of disorder irrelevance for inhomogeneous pinning models with return exponent $ \alpha \in (0, 1 / 2) $. We also give a new upper bound for the contact fraction of the disordered model at criticality.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Pinning/Wetting Models, Disordered Models, Harris Criterion, Relevant Disorder, Renewal Theory", } @Article{Balan:2010:ECC, author = "Raluca Balan and Sana Louhichi", title = "Explicit Conditions for the Convergence of Point Processes Associated to Stationary Arrays", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "39:428--39:441", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1563", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1563", abstract = "In this article, we consider a stationary array of random variables (which satisfy some asymptotic independence conditions), and the corresponding sequence of point processes. Our main result identifies some explicit conditions for the convergence of the sequence of point processes in terms of the probabilistic behavior of the variables in the array.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "infinite divisibility, point process, asymptotic independence, weak convergence, extremal index", } @Article{vandenBerg:2010:ERD, author = "Jacob van den Berg and Marcelo Hil{\'a}rio and Alexander Holroyd", title = "Escape of resources in a distributed clustering process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "40:442--40:448", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1567", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1567", abstract = "In a distributed clustering algorithm introduced by Coffman, Courtois, Gilbert and Piret [1], each vertex of $ \mathbb {Z}^d $ receives an initial amount of a resource, and, at each iteration, transfers all of its resource to the neighboring vertex which currently holds the maximum amount of resource. In [4] it was shown that, if the distribution of the initial quantities of resource is invariant under lattice translations, then the flow of resource at each vertex eventually stops almost surely, thus solving a problem posed in [2]. In this article we prove the existence of translation-invariant initial distributions for which resources nevertheless escape to infinity, in the sense that the final amount of resource at a given vertex is strictly smaller in expectation than the initial amount. This answers a question posed in [4].", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Clustering process, random spanning tree", } @Article{Markstrom:2010:CPN, author = "Klas Markstr{\"o}m", title = "Closure Properties and Negatively Associated Measures violating the {van den Berg--Kesten} Inequality", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "41:449--41:456", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1575", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1575", abstract = "We first give an example of a negatively associated measure which does not satisfy the van den Berg-Kesten inequality. Next we show that the class of measures satisfying the van den Berg-Kesten inequality is not closed under either of conditioning, introduction of external fields or convex combinations. Finally we show that this class also includes measure which have rank sequence which is not logconcave.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Negative correlation, Correlation Inequalities, Closure properties", } @Article{DOvidio:2010:ESF, author = "Mirko D'Ovidio", title = "Explicit solutions to fractional differential equations via generalized gamma convolution", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "42:457--42:474", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1570", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1570", abstract = "In this paper we deal with Mellin convolution of generalized Gamma densities which leads to integrals of modified Bessel functions of the second kind. Such convolutions allow us to explicitly write the solutions of the time-fractional diffusion equations involving the adjoint operators of a square Bessel process and a Bessel process", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Mellin convolution formula, generalized Gamma r.v.'s, Stable subordinators, Fox functions, Bessel processes, Modified Bessel functions", } @Article{Best:2010:ASM, author = "Katharina Best and Peter Pfaffelhuber", title = "The {Aldous--Shields} model revisited with application to cellular ageing", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "43:475--43:488", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1581", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1581", abstract = "In Aldous and Shields (1988) a model for a rooted, growing random binary tree with edge lengths 1 was presented. For some $ c > 0 $, an external vertex splits at rate $ c^{-i} $ (and becomes internal) if its distance from the root (depth) is $i$. We reanalyse the tree profile for $ c > 1$, i.e. the numbers of external vertices in depth $ i = 1, 2, \ldots {}$. Our main results are concrete formulas for the expectation and covariance-structure of the profile. In addition, we present the application of the model to cellular ageing. Here, we say that nodes in depth $ h + 1$ are senescent, i.e. do not split. We obtain a limit result for the proportion of non-senesced vertices for large $h$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "cellular senescence; Hayflick limit; Random tree; telomere", } @Article{Olivier:2010:DIS, author = "Wintenberger Olivier", title = "Deviation inequalities for sums of weakly dependent time series", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "44:489--44:503", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1577", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1577", abstract = "In this paper we give new deviation inequalities for the partial sums of weakly dependent data. The loss from the independent case is studied carefully. We give examples of non mixing time series such that dynamical systems and Bernoulli shifts for whom such deviation inequality holds. The proofs are based on the blocks technique and different coupling arguments.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Bernoulli shifts; Bernstein's type inequalities; coupling schemes; expanding maps; Markov chains; weak dependence", } @Article{Freij:2010:POS, author = "Ragnar Freij and Johan W{\"a}stlund", title = "Partially ordered secretaries", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "45:504--45:507", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1579", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1579", abstract = "The elements of a finite nonempty partially ordered set are exposed at independent uniform times in $ [0, 1] $ to a selector who, at any given time, can see the structure of the induced partial order on the exposed elements. The selector's task is to choose online a maximal element. This generalizes the classical linear order secretary problem, for which it is known that the selector can succeed with probability $ 1 / e $ and that this is best possible. We describe a strategy for the general problem that achieves success probability at least $ 1 / e $ for an arbitrary partial order.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "best choice problem; partial order.; secretary problem", } @Article{Osekowski:2010:STI, author = "Adam Osekowski", title = "Sharp tail inequalities for nonnegative submartingales and their strong differential subordinates", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "46:508--46:521", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1582", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1582", abstract = "Let $ f = (f_n)_{n \geq 0} $ be a nonnegative submartingale starting from $x$ and let $ g = (g_n)_{n \geq 0}$ be a sequence starting from $y$ and satisfying\par $$ |d g_n| \leq |d f_n|, \quad | \mathbb {E}(d g_n| \mathcal {F}_{n - 1})| \leq \mathbb {E}(d f_n| \mathcal {F}_{n - 1}) $$ for $ n \geq 1$. We determine the best universal constant $ U(x, y)$ such that\par $$ \mathbb {P}(\sup_n g_n \geq 0) \leq ||f||_1 + U(x, y). $$ As an application, we deduce a sharp weak type $ (1, 1)$ inequality for the one-sided maximal function of $g$ and determine, for any $ t \in [0, 1]$ and $ \beta \in \mathbb {R}$, the number\par $$ L(x, y, t, \beta) = \inf \{ ||f||_1 : \mathbb {P}(\sup_n g_n \geq \beta) \geq t \} . $$ The estimates above yield analogous statements for stochastic integrals in which the integrator is a nonnegative submartingale. The results extend some earlier work of Burkholder and Choi in the martingale setting.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Strong differential subordination; Submartingale; Weak-type inequality", } @Article{Aidekon:2010:TAT, author = "Elie Aidekon", title = "Tail asymptotics for the total progeny of the critical killed branching random walk", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "47:522--47:533", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1583", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1583", abstract = "We consider a branching random walk on $R$ with a killing barrier at zero. At criticality, the process becomes eventually extinct, and the total progeny $Z$ is therefore finite. We show that $ P(Z > n)$ is of order $ (n \ln^2 (n))^{-1}$, which confirms the prediction of Addario-Berry and Broutin [1].", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Branching random walk, total progeny.", } @Article{Caravenna:2010:LDP, author = "Francesco Caravenna and Martin Borecki", title = "Localization for $ (1 + 1)$-dimensional pinning models with {$ (\nabla + \Delta)$}-interaction", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "48:534--48:548", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1584", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1584", abstract = "We study the localization/delocalization phase transition in a class of directed models for a homogeneous linear chain attracted to a defect line. The self-interaction of the chain is of mixed gradient and Laplacian kind, whereas the attraction to the defect line is of $ \delta $-pinning type, with strength $ \epsilon \ge 0$. It is known that, when the self-interaction is purely Laplacian, such models undergo a {\em non-trivial\/} phase transition: to localize the chain at the defect line, the reward $ \epsilon $ must be greater than a strictly positive critical threshold $ \epsilon_c > 0$. On the other hand, when the self-interaction is purely gradient, it is known that the transition is {\em trivial\/}: an arbitrarily small reward $ \epsilon > 0$ is sufficient to localize the chain at the defect line ($ \epsilon_c = 0$). In this note we show that in the mixed gradient and Laplacian case, under minimal assumptions on the interaction potentials, the transition is always trivial, that is $ \epsilon_c = 0$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Free Energy; Gradient Interaction; Laplacian Interaction; Linear Chain Model; Localization Phenomena; Markov Chain; Phase Transition; Pinning Model; Polymer Model", } @Article{Delyon:2010:CIS, author = "Bernard Delyon", title = "Concentration inequalities for the spectral measure of random matrices", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "49:549--49:562", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1585", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1585", abstract = "We give new exponential inequalities for the spectral measure of random Wishart matrices. These results give in particular useful bounds when these matrices have the form $ M = Y Y^T $, in the case where $Y$ is a $ p \times n$ random matrix with independent enties (weaker conditions are also proposed), and $p$ and $n$ are large.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "random matrices; Spectral measure", } @Article{Tassy:2010:RIG, author = "Martin Tassy", title = "Random interlacements on {Galton--Watson} Trees", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "50:562--50:571", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1586", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1586", abstract = "We study the critical parameter $ u^* $ of random interlacements on a Galton--Watson tree conditioned on the non-extinction event. We show that, for a given law of a Galton--Watson tree, the value of this parameter is a.s. constant and non-trivial. We also characterize this value as the solution of a certain equation.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random Interlacement, Galton--Watson tree, critical behaviour", } @Article{Savov:2010:RIL, author = "Mladen Savov and Matthias Winkel", title = "Right inverses of {L{\'e}vy} processes: the excursion measure in the general case", journal = j-ELECTRON-COMMUN-PROBAB, volume = "15", pages = "51:572--51:584", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v15-1590", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1590", abstract = "This article is about right inverses of L{\'e}vy processes as first introduced by Evans in the symmetric case and later studied systematically by the present authors and their co-authors. Here we add to the existing fluctuation theory an explicit description of the excursion measure away from the (minimal) right inverse. This description unifies known formulas in the case of a positive Gaussian coefficient and in the bounded variation case. While these known formulas relate to excursions away from a point starting negative continuously, and excursions started by a jump, the present description is in terms of excursions away from the supremum continued up to a return time. In the unbounded variation case with zero Gaussian coefficient previously excluded, excursions start negative continuously, but the excursion measures away from the right inverse and away from a point are mutually singular. We also provide a new construction and a new formula for the Laplace exponent of the minimal right inverse.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "L{\'e}vy process, right inverse, subordinator, fluctuation theory, excursion", } @Article{Kuhn:2011:OPN, author = "Christoph K{\"u}hn and Marc Teusch", title = "Optional processes with non-exploding realized power variation along stopping times are l{\`a}gl{\`a}d", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "1:1--1:8", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1591", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1591", abstract = "We prove that an optional process of non-exploding realized power variation along stopping times possesses almost surely l{\`a}gl{\`a}d paths. This result is useful for the analysis of some imperfect market models in mathematical finance. In the finance applications variation naturally appears along stopping times and not pathwise. On the other hand, if the power variation were only taken along deterministic points in time, the assertion would obviously be wrong.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "power variation, path properties, stopping times", } @Article{Osekowski:2011:RAD, author = "Adam Osekowski", title = "On relaxing the assumption of differential subordination in some martingale inequalities", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "2:9--2:21", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1593", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1593", abstract = "Let $X$, $Y$ be continuous-time martingales taking values in a se\-pa\-rable Hilbert space $ \mathcal {H}$.\par (i) Assume that $X$, $Y$ satisfy the condition $ [X, X]_t \geq [Y, Y]_t$ for all $ t \geq 0$. We prove the sharp inequalities\par $$ \sup_t||Y_t||_p \leq (p - 1)^{-1} \sup_t||X_t||_p, \qquad 1 < p \leq 2, $$ $$ \mathbb {P}(\sup_t|Y_t| \geq 1) \leq \frac {2}{\Gamma (p + 1)} \sup_t||X_t||_p^p, \qquad 1 \leq p \leq 2, $$ and for any $ K > 0$ we determine the optimal constant $ L = L(K)$ depending only on $K$ such that\par $$ \sup_t ||Y_t||_1 \leq K \sup_t \mathbb {E}|X_t| \log |X_t| + L(K). $$ (ii) Assume that $X$, $Y$ satisfy the condition $ [X, X]_\infty - [X, X]_{t-} \geq [Y, Y]_\infty - [Y, Y]_{t-}$ for all $ t \geq 0$. We establish the sharp bounds\par $$ \sup_t||Y_t||_p \leq (p - 1) \sup_t||X_t||_p, \qquad 2 \leq p < \infty $$ and\par $$ \mathbb {P}(\sup_t|Y_t| \geq 1) \leq \frac {p^{p - 1}}{2} \sup_t||X_t||_p^p, \qquad 2 \leq p < \infty . $$ \par This generalizes the previous results of Burkholder, Suh and the author, who showed the above estimates under the more restrictive assumption of differential subordination. The proof is based on Burkholder's technique and integration method.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "differential subordination; Martingale; moment inequality; weak-type inequality", } @Article{Couronne:2011:CSP, author = "Olivier Couronn{\'e} and Nathana{\"e}l Enriquez and Lucas Gerin", title = "Construction of a short path in high-dimensional first passage percolation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "3:22--3:28", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1595", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1595", abstract = "For first passage percolation in $ \mathbb {Z}^d $ with large $d$, we construct a path connecting the origin to $ \{ x_1 = 1 \} $, whose passage time has optimal order $ \log d / d$. Besides, an improved lower bound for the {"diagonal"} speed of the cluster combined with a result by Dhar (1988) shows that the limiting shape in FPP with exponential passage times (and thus that of Eden model) is not the Euclidean ball in dimension larger than 35.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "first passage percolation; limit shape; time constant", } @Article{Backhausz:2011:LDD, author = "Agnes Backhausz", title = "Limit distribution of degrees in random family trees", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "4:29--4:37", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1598", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1598", abstract = "In a one-parameter model for evolution of random trees, which also includes the Barabasi-Albert random tree [1], almost sure behavior and the limiting distribution of the degree of a vertex in a fixed position are examined. A functional central limit theorem is also given. Results about Polya urn models are applied in the proofs.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "preferential attachment; random trees; urn models", } @Article{Tkocz:2011:GMD, author = "Tomasz Tkocz", title = "{Gaussian} measures of dilations of convex rotationally symmetric sets in {$ \mathbb {C}^n $}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "5:38--5:49", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1599", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1599", abstract = "We consider the complex case of the {\em S-inequality\/}. It concerns the behaviour of Gaussian measures of dilations of convex and rotationally symmetric sets in $ \mathbb {C}^n $. We pose and discuss a conjecture that among all such sets measures of cylinders decrease the fastest under dilations. Our main result in this paper is that this conjecture holds under the additional assumption that the Gaussian measure of the sets considered is not greater than some constant $ c > 0.64 $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Gaussian measure, convex bodies, isoperimetric inequalities", } @Article{Defosseux:2011:GLU, author = "Manon Defosseux", title = "Generalized {Laguerre} Unitary Ensembles and an interacting particles model with a wall", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "6:59--6:69", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1602", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1602", abstract = "We introduce and study a new interacting particles model with a wall and two kinds of interactions --- blocking and pushing --- which maintain particles in a certain order. We show that it involves a random matrix model.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Gelfand-Tsetlin patterns; interacting particles system with a wall; interlacing; intertwining; random matrices", } @Article{Ghosh:2011:ASB, author = "Subhankar Ghosh and Larry Goldstein", title = "Applications of size biased couplings for concentration of measures", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "7:70--7:83", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1605", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1605", abstract = "Let $Y$ be a nonnegative random variable with mean $ \mu $ and finite positive variance $ \sigma^2$, and let $ Y^s$, defined on the same space as $Y$, have the $Y$ size biased distribution, that is, the distribution characterized by\par $$ E[Y f(Y)] = \mu E f(Y^s) \quad \mbox {for all functions {\em f} for which these expectations exist.} $$ Under a variety of conditions on the coupling of $Y$ and $ Y^s$, including combinations of boundedness and monotonicity, concentration of measure inequalities such as\par $$ P \left (\frac {Y - \mu }{\sigma } \ge t \right) \le \exp \left ( - \frac {t^2}{2(A + Bt)} \right) \quad \mbox {for all $ t \ge 0$ } $$ are shown to hold for some explicit $A$ and $B$ in \cite{cnm}. Such concentration of measure results are applied to a number of new examples: the number of relatively ordered subsequences of a random permutation, sliding window statistics including the number of $m$-runs in a sequence of coin tosses, the number of local maxima of a random function on a lattice, the number of urns containing exactly one ball in an urn allocation model, and the volume covered by the union of $n$ balls placed uniformly over a volume $n$ subset of $ \mathbb {R}^d$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Hubalek:2011:CSR, author = "Friedrich Hubalek and Alexey Kuznetsov", title = "A convergent series representation for the density of the supremum of a stable process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "8:84--8:95", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1601", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1601", abstract = "We study the density of the supremum of a strictly stable L{\'e}vy process. We prove that for almost all values of the index $ \alpha $ - except for a dense set of Lebesgue measure zero - the asymptotic series which were obtained in Kuznetsov (2010) {"On} extrema of stable {processes"} are in fact absolutely convergent series representations for the density of the supremum.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "stable processes, supremum, Mellin transform, double Gamma function, Liouville numbers, continued fractions", } @Article{Rio:2011:ACM, author = "Emmanuel Rio", title = "Asymptotic constants for minimal distance in the central limit theorem", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "9:96--9:103", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1609", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1609", abstract = "In this paper, we generalize the asymptotic result of Ess{\'e}en (1958) concerning the Wasserstein distance of order one in the mean central limit theorem to the Wasserstein distances of order $r$ for $ r \in]1, 2]$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Minimal metric, Wasserstein distance, Cornish-Fisher expansion of first order, Ess{\'e}en's mean central limit theorem, Global central limit theorem", } @Article{Bordenave:2011:SSP, author = "Charles Bordenave", title = "On the spectrum of sum and product of non-{Hermitian} random matrices", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "10:104--10:113", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1606", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1606", abstract = "In this note, we revisit the work of T. Tao and V. Vu on large non-Hermitian random matrices with independent and identically distributed (i.i.d.) entries with mean zero and unit variance. We prove under weaker assumptions that the limit spectral distribution of sum and product of non-Hermitian random matrices is universal. As a byproduct, we show that the generalized eigenvalues distribution of two independent matrices converges almost surely to the uniform measure on the Riemann sphere.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "generalized eigenvalues, non-Hermitian random matrices, spherical law", } @Article{Bolthausen:2011:RTM, author = "Erwin Bolthausen and Jean-Dominique Deuschel and Ofer Zeitouni", title = "Recursions and tightness for the maximum of the discrete, two dimensional {Gaussian} free field", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "11:114--11:119", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1610", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1610", abstract = "We consider the maximum of the discrete two dimensional Gaussian free field in a box, and prove the existence of a (dense) deterministic subsequence along which the maximum, centered at its mean, is tight. The method of proof relies on an argument developed by Dekking and Host for branching random walks with bounded increments and on comparison results specific to Gaussian fields.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Gaussian free field. Recursions.", } @Article{Chassagneux:2011:NEU, author = "Jean Fran{\c{c}}ois Chassagneux and Romuald Elie and Idris Kharroubi", title = "A note on existence and uniqueness for solutions of multidimensional reflected {BSDEs}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "12:120--12:128", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1614", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1614", abstract = "In this note, we provide an innovative and simple approach for proving the existence of a unique solution for multidimensional reflected BSDEs associated to switching problems. Getting rid of a monotonicity assumption on the driver function, this approach simplifies and extends the recent results of Hu and Tang (2008) or Hamadene and Zhang (2010).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "BSDE with oblique reflections; Switching problems", } @Article{Miranda:2011:GCL, author = "Yuri Mejia Miranda and Gordon Slade", title = "The growth constants of lattice trees and lattice animals in high dimensions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "13:129--13:136", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1612", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1612", abstract = "We prove that the growth constants for nearest-neighbour lattice trees and lattice (bond) animals on the integer lattice $ \mathbb {Z}^d $ are asymptotic to $ 2 d e $ as the dimension goes to infinity, and that their critical one-point functions converge to $e$. Similar results are obtained in dimensions $ d > 8$ in the limit of increasingly spread-out models; in this case the result for the growth constant is a special case of previous results of M. Penrose. The proof is elementary, once we apply previous results of T. Hara and G. Slade obtained using the lace expansion.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "growth constant; lattice animal; lattice tree; mean-field model", } @Article{Demni:2011:KRV, author = "Nizar Demni", title = "{Kanter} random variable and positive free stable distributions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "14:137--14:149", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1608", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1608", abstract = "According to a representation due to M. Kanter, the density of some power of a positive stable distribution is a completely monotone function. In this paper, we first derive its representative Bernstein measure which also describes the law of some function of a uniform random variable, referred to below as the Kanter random variable. Then, the distribution function of the latter variable is written down and gives a more explicit description of the non commutative analogue of positive stable distributions in the setting of Voiculescu's free probability theory. Analytic evidences of the occurrence of the Kanter random variable in both the classical and the free settings conclude the exposition.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stable laws, free probability, Fox H-function", } @Article{Hahn:2011:TCG, author = "Marjorie Hahn and Jelena Ryvkina and Kei Kobayashi and Sabir Umarov", title = "On time-changed {Gaussian} processes and their associated {Fokker--Planck--Kolmogorov} equations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "15:150--15:164", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1620", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1620", abstract = "This paper establishes Fokker--Planck-Kolmogorov type equations for time-changed Gaussian processes. Examples include those equations for a time-changed fractional Brownian motion with time-dependent Hurst parameter and for a time-changed Ornstein--Uhlenbeck process. The time-change process considered is the inverse of either a stable subordinator or a mixture of independent stable subordinators.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Fokker--Planck equation; fractional Brownian motion; Gaussian process; inverse subordinator; Kolmogorov equation; time-change; time-dependent Hurst parameter; Volterra process", } @Article{Jung:2011:IFS, author = "Paul Jung", title = "Indicator fractional stable motions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "16:165--16:173", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1611", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1611", abstract = "Using the framework of random walks in random scenery, Cohen and Samorodnitsky (2006) introduced a family of symmetric $ \alpha $-stable motions called local time fractional stable motions. When $ \alpha = 2$, these processes are precisely fractional Brownian motions with $ 1 / 2 < H < 1$. Motivated by random walks in alternating scenery, we find a complementary family of symmetric $ \alpha $-stable motions which we call indicator fractional stable motions. These processes are complementary to local time fractional stable motions in that when $ \alpha = 2$, one gets fractional Brownian motions with $ 0 < H < 1 / 2$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "fractional Brownian motion; local time fractional stable motion; random reward schema; random walk in random scenery; self-similar process; stable process", } @Article{Depperschmidt:2011:MMM, author = "Andrej Depperschmidt and Andreas Greven and Peter Pfaffelhuber", title = "Marked metric measure spaces", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "17:174--17:188", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1615", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1615", abstract = "A marked metric measure space (mmm-space) is a triple $ (X, r, \mu) $, where $ (X, r) $ is a complete and separable metric space and $ \mu $ is a probability measure on $ X \times I $ for some Polish space $I$ of possible marks. We study the space of all (equivalence classes of) marked metric measure spaces for some fixed $I$. It arises as a state space in the construction of Markov processes which take values in random graphs, e.g. tree-valued dynamics describing randomly evolving genealogical structures in population models. We derive here the topological properties of the space of mmm-spaces needed to study convergence in distribution of random mmm-spaces. Extending the notion of the Gromov-weak topology introduced in (Greven, Pfaffelhuber and Winter, 2009), we define the marked Gromov-weak topology, which turns the set of mmm-spaces into a Polish space. We give a characterization of tightness for families of distributions of random mmm-spaces and identify a convergence determining algebra of functions, called polynomials.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Metric measure space, Gromov metric triples, Gromov- weak topology, Prohorov metric, Population model", } @Article{Bass:2011:CMH, author = "Richard Bass", title = "Correction to {``The measurability of hitting times''}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "18:189--18:191", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1627", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", note = "See \cite{Bass:2010:MHT}.", URL = "http://ecp.ejpecp.org/article/view/1627", abstract = "We correct an error in \url{http://www.math.washington.edu/~ejpecp/ECP/viewarticle.php?id=2181&layout=abstract} Electronic Communications in Probability, Vol 15 (2010), paper 10.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stopping time, hitting time, progressively measurable, optional, predictable, debut theorem, section theorem", } @Article{Neunhauserer:2011:FEP, author = "J{\"o}rg Neunh{\"a}userer", title = "A family of exceptional parameters for non-uniform self-similar measures", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "19:192--19:199", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1618", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib; http://www.math.utah.edu/pub/tex/bib/mathematica.bib", URL = "http://ecp.ejpecp.org/article/view/1618", abstract = "We present plane algebraic curves that have segments of points for which non uniform self-similar measures get singular. We calculate appropriate points on the curves using Mathematica. These points are in the parameter domain where we generically have absolute continuity of the measures.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Non-uniform self similar measures, singularity, algebraic curves", } @Article{Graversen:2011:RUC, author = "Svend-Erik Graversen and Jan Pedersen", title = "Representations of {Urbanik}'s classes and multiparameter {Ornstein--Uhlenbeck} processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "20:200--20:212", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1621", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1621", abstract = "A class of integrals with respect to homogeneous L{\'e}vy bases on $ \mathbb {R}^k $ is considered. In the one-dimensional case $ k = 1 $ this class corresponds to the selfdecomposable distributions. Necessary and sufficient conditions for existence as well as some representations of the integrals are given. Generalizing the one-dimensional case it is shown that the class of integrals corresponds to Urbanik's class $ L_{k - 1}(R) $. Finally, multiparameter Ornstein--Uhlenbeck processes are defined and studied.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "L{\'e}vy bases; multiparameter Ornstein--Uhlenbeck processes; stochastic integrals; Urbanik's classes", } @Article{Debussche:2011:AFE, author = "Arnaud Debussche and Michael Hoegele and Peter Imkeller", title = "Asymptotic first exit times of the {Chafee--Infante} equation with small heavy-tailed {L{\'e}vy} noise", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "21:213--21:225", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1622", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1622", abstract = "This article studies the behavior of stochastic reaction-diffusion equations driven by additive regularly varying pure jump L{\'e}vy noise in the limit of small noise intensity. It is shown that the law of the suitably renormalized first exit times from the domain of attraction of a stable state converges to an exponential law of parameter 1 in a strong sense of Laplace transforms, including exponential moments. As a consequence, the expected exit times increase polynomially in the inverse intensity, in contrast to Gaussian perturbations, where this growth is known to be of exponential rate.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "first exit times; regularly varying L{\'e}vy process; small noise asymptotics; stochastic reaction diffusion equation with heavy-tailed L{\'e}vy noise", } @Article{Ben-Ari:2011:SSM, author = "Iddo Ben-Ari and Anastasios Matzavinos and Alexander Roitershtein", title = "On a species survival model", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "22:226--22:233", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1625", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1625", abstract = "In this paper we provide some sharp asymptotic results for a stochastic model of species survival recently proposed by Guiol, Machado, and Schinazi.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Bak-Sneppen model; birth and death process; central limit theorem; evolution; law of iterated logarithm; population genetics", } @Article{Menozzi:2011:PTM, author = "Stephane Menozzi", title = "Parametrix techniques and martingale problems for some degenerate {Kolmogorov} equations", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "23:234--23:250", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1619", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1619", abstract = "We prove the uniqueness of the martingale problem associated to some degenerate operators. The key point is to exploit the strong parallel between the new technique introduced by Bass and Perkins [BP09] to prove uniqueness of the martingale problem in the framework of non- degenerate elliptic operators and the Mc Kean and Singer [MS67] parametrix approach to the density expansion that has previously been extended to the degenerate setting that we consider (see Delarue and Menozzi [DM10]).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Parametrix techniques, Martingale problem, hypoelliptic equations", } @Article{Peres:2011:RTE, author = "Yuval Peres and Sebastien Roch", title = "Reconstruction on Trees: Exponential Moment Bounds for Linear Estimators", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "24:251--24:261", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1630", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1630", abstract = "Consider a Markov chain $ (\xi_v)_{v \in V} \in [k]^V $ on the infinite $b$-ary tree $ T = (V, E)$ with irreducible edge transition matrix $M$, where $ b \geq 2$, $ k \geq 2$ and $ [k] = \{ 1, \ldots, k \} $. We denote by $ L_n$ the level-$n$ vertices of $T$. Assume $M$ has a real second-largest (in absolute value) eigenvalue $ \lambda $ with corresponding real eigenvector $ \nu \neq 0$. Letting $ \sigma_v = \nu_{\xi_v}$, we consider the following root-state estimator, which was introduced by Mossel and Peres (2003) in the context of the ``recontruction problem'' on trees: \begin{equation*} S_n = (b\lambda)^{-n} \sum_{x\in L_n} \sigma_x. \end{equation*} As noted by Mossel and Peres, when $ b \lambda^2 > 1$ (the so-called Kesten-Stigum reconstruction phase) the quantity $ S_n$ has uniformly bounded variance. Here, we give bounds on the moment-generating functions of $ S_n$ and $ S_n^2$ when $ b \lambda^2 > 1$. Our results have implications for the inference of evolutionary trees.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Markov chains on trees, reconstruction problem, Kesten-Stigum bound, phylogenetic reconstruction", } @Article{Tropp:2011:FIM, author = "Joel Tropp", title = "{Freedman}'s inequality for matrix martingales", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "25:262--25:270", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1624", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1624", abstract = "Freedman's inequality is a martingale counterpart to Bernstein's inequality. This result shows that the large-deviation behavior of a martingale is controlled by the predictable quadratic variation and a uniform upper bound for the martingale difference sequence. Oliveira has recently established a natural extension of Freedman's inequality that provides tail bounds for the maximum singular value of a matrix-valued martingale. This note describes a different proof of the matrix Freedman inequality that depends on a deep theorem of Lieb from matrix analysis. This argument delivers sharp constants in the matrix Freedman inequality, and it also yields tail bounds for other types of matrix martingales. The new techniques are adapted from recent work by the present author.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Discrete-time martingale, large deviation, probability inequality, random matrix", } @Article{Blath:2011:SEC, author = "Jochen Blath and Noemi Kurt", title = "Survival and extinction of caring double-branching annihilating random walk", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "26:271--26:282", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1631", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1631", abstract = "Branching annihilating random walk (BARW) is a generic term for a class of interacting particle systems on $ \mathbb {Z}^d $ in which, as time evolves, particles execute random walks, produce offspring (on neighbouring sites) and (instantaneously) disappear when they meet other particles. Much of the interest in such models stems from the fact that they typically lack a monotonicity property called {\em attractiveness\/}, which in general makes them exceptionally hard to analyse and in particular highly sensitive in their qualitative long-time behaviour to even slight alterations of the branching and annihilation mechanisms. In this short note, we introduce so-called {\em caring\/} double-branching annihilating random walk (cDBARW) on $ \mathbb {Z} $, and investigate its long-time behaviour. It turns out that it either allows survival with positive probability if the branching rate is greater than $ 1 / 2 $, or a.s. extinction if the branching rate is smaller than $ 1 / 3 $ and (additionally) branchings are only admitted for particles which have at least one neighbouring particle (so-called 'cooperative branching'). Further, we show a.s. extinction for all branching rates for a variant of this model, where branching is only allowed if offspring can be placed at odd distance between each other. It is the latter (extinction-type) results which seem remarkable, since they appear to hint at a general extinction result for a non-trivial parameter range in the so-called 'parity-preserving universality class', suggesting the existence of a 'true' phase transition. The rigorous proof of such a non-trivial phase transition remains a particularly challenging open problem.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Branching Annihilating Random Walk, extinction, survival, interface duality, swapping voter model", } @Article{Junglen:2011:QBA, author = "Stefan Junglen", title = "Quantization Balls and Asymptotics of Quantization Radii for Probability Distributions with Radial Exponential Tails", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "27:283--27:295", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1629", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1629", abstract = "In this paper, we provide the sharp asymptotics for the {\em quantization radius (maximal radius)\/} for a sequence of {\em optimal quantizers\/} for random variables $X$ in $ (\mathbb {R}^d, \| \, \cdot \, \|)$ with radial exponential tails. This result sharpens and generalizes the results developed for the quantization radius in [4] for $ d > 1$, where the weak asymptotics is established for similar distributions in the Euclidean case. Furthermore, we introduce {\em quantization balls\/}, which provide a more general way to describe the asymptotic geometric structure of optimal codebooks, and extend the terminology of the quantization radius.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Aurzada:2011:MRT, author = "Frank Aurzada and Hanna D{\"o}ring and Marcel Ortgiese and Michael Scheutzow", title = "Moments of recurrence times for {Markov} chains", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "28:296--28:303", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1632", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1632", abstract = "We consider moments of the return times (or first hitting times) in an irreducible discrete time discrete space Markov chain. It is classical that the finiteness of the first moment of a return time of one state implies the finiteness of the first moment of the first return time of any other state. We extend this statement to moments with respect to a function $f$, where $f$ satisfies a certain, best possible condition. This generalizes results of K. L. Chung (1954) who considered the functions $ f(n) = n^p$ and wondered ``[\ldots{}] what property of the power $ n^p$ lies behind this theorem [\ldots{}]'' (see Chung (1967), p. 70). We exhibit that exactly the functions that do not increase exponentially - neither globally nor locally - fulfill the above statement.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Discrete time Markov chain, recurrence time, generalized moment", } @Article{Barbu:2011:RTP, author = "Viorel Barbu and Giuseppe {Da Prato} and Luciano Tubaro", title = "A Reflection Type Problem for the Stochastic {$2$-D} {Navier--Stokes} Equations with Periodic Conditions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "29:304--29:313", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1633", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1633", abstract = "We prove the existence of a solution for the Kolmogorov equation associated with a reflection problem for {$2$-D} stochastic Navier--Stokes equations with periodic spatial conditions and the corresponding stream flow in a closed ball of a Sobolev space of the torus $ T^2 $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "{$2$-D} stochastic Navier--Stokes equations, Gibbs measures, Kolmogorov operator", } @Article{Dallaporta:2011:NCL, author = "Sandrine Dallaporta and Van Vu", title = "A note on the {Central Limit Theorem} for the Eigenvalue Counting Function of {Wigner} Matrices", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "30:214--30:322", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1634", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1634", abstract = "The purpose of this note is to establish a Central Limit Theorem for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on the correct asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson, and its extension to large families of Wigner matrices by means of the Tao and Vu Four Moment Theorem and recent localization results by Erd?s, Yau and Yin.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Central Limit Theorem; eigenvalue counting function; Four Moment Theorem; localization; random matrices", } @Article{Heil:2011:RLB, author = "Hadrian Heil and Makoto Nakashima", title = "A Remark on Localization for Branching Random Walks in Random Environment", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "31:323--31:336", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1603", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1603", abstract = "We prove a localization-result for branching random walks in random environment, namely that if the process does not die out, the most populated site will infinitely often contain more than a fixed percentage of the population. This had been proven already before by Hu and Yoshida, but it is possible to drop their assumption that particles may not die.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "branching random walk; localization; random environment", } @Article{Fournier:2011:SSH, author = "Nicolas Fournier and Jacques Printems", title = "Stability of the stochastic heat equation in {$ L^1 ([0, 1]) $}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "32:337--32:352", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1636", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1636", abstract = "We consider the white-noise driven stochastic heat equation on $ [0, 1] $ with Lipschitz-continuous drift and diffusion coefficients. We derive an inequality for the $ L^1 ([0, 1])$-norm of the difference between two solutions. Using some martingale arguments, we show that this inequality provides some estimates which allow us to study the stability of the solution with respect the initial condition, the uniqueness of the possible invariant distribution and the asymptotic confluence of solutions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Tucci:2011:API, author = "Gabriel Tucci", title = "Asymptotic Products of Independent {Gaussian} Random Matrices with Correlated Entries", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "33:353--33:364", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1635", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1635", abstract = "In this work we address the problem of determining the asymptotic spectral measure of the product of independent, Gaussian random matrices with correlated entries, as the dimension and the number of multiplicative terms goes to infinity. More specifically, let $ \{ X_p(N) \}_{p = 1}^\infty $ be a sequence of $ N \times N $ independent random matrices with independent and identically distributed Gaussian entries of zero mean and variance $ \frac {1}{\sqrt {N}} $. Let $ \{ \Sigma (N) \}_{N = 1}^\infty $ be a sequence of $ N \times N $ deterministic and Hermitian matrices such that the sequence converges in moments to a compactly supported probability measure $ \sigma $. Define the random matrix $ Y_p(N) $ as $ Y_p(N) = X_p(N) \Sigma (N) $. This is a random matrix with correlated Gaussian entries and covariance matrix $ E(Y_p(N)^*Y_p(N)) = \Sigma (N)^2 $ for every $ p \geq 1 $. The positive definite $ N \times N $ matrix\par $$ B_n^{1 / (2n)} (N) := \left (Y_1^* (N) Y_2^* (N) \dots Y_n^*(N) Y_n(N) \dots Y_2 (N) Y_1 (N) \right)^{1 / (2n)} \to \nu_n $$ converges in distribution to a compactly supported measure in $ [0, \infty) $ as the dimension of the matrices $ N \to \infty $. We show that the sequence of measures $ \nu_n $ converges in distribution to a compactly supported measure $ \nu_n \to \nu $ as $ n \to \infty $. The measures $ \nu_n $ and $ \nu $ only depend on the measure $ \sigma $. Moreover, we deduce an exact closed-form expression for the measure $ \nu $ as a function of the measure $ \sigma $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Limit Measures; Lyapunov Exponents; MIMO systems; Random Matrices", } @Article{Bourguin:2011:CTG, author = "Solesne Bourguin and Ciprian Tudor", title = "Cram{\'e}r theorem for Gamma random variables", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "34:365--34:378", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1639", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1639", abstract = "In this paper we discuss the following problem: given a random variable $ Z = X + Y $ with Gamma law such that $X$ and $Y$ are independent, we want to understand if then $X$ and $Y$ each follow a Gamma law. This is related to Cramer's theorem which states that if $X$ and $Y$ are independent then $ Z = X + Y$ follows a Gaussian law if and only if $X$ and $Y$ follow a Gaussian law. We prove that Cramer's theorem is true in the Gamma context for random variables living in a Wiener chaos of fixed order but the result is not true in general. We also give an asymptotic variant of our result.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Cram{\'e}r's theorem, Gamma distribution, multiple stochastic integrals, limit theorems, Malliavin calculus", } @Article{Rath:2011:TRI, author = "Balazs Rath and Artem Sapozhnikov", title = "On the transience of random interlacements", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "35:379--35:391", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1637", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1637", abstract = "We consider the interlacement Poisson point process on the space of doubly-infinite $ \mathbb {Z}^d$-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least one of these trajectories is the graph induced by the random interlacements at level $u$ of Sznitman(2010). We prove that for any $ u > 0$, almost surely, the random interlacement graph is transient.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "capacity.; intersection of random walks; Random interlacement; random walk; resistance; transience", } @Article{Aurzada:2011:OSE, author = "Frank Aurzada", title = "On the one-sided exit problem for fractional {Brownian} motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "36:392--36:404", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1640", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1640", abstract = "We consider the one-sided exit problem for fractional Brownian motion (FBM), which is equivalent to the question of the distribution of the lower tail of the maximum of FBM on the unit interval. We improve the bounds given by Molchan (1999) and shed some light on the relation to the quantity I studied there.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "First passage time; fractional Brownian motion; lower tail probability; one-sided barrier problem; one-sided exit problem; small value probability; survival exponent", } @Article{Bose:2011:HIH, author = "Arup Bose and Rajat Hazra and Koushik Saha", title = "Half Independence and half cumulants", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "37:405--37:422", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1651", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1651", abstract = "The notion of half independence arises in random matrices and quantum groups. This notion is available only for elements of a noncommutative probability space and assumes the existence of all moments. We relate half independence to a certain class of partitions and use it to define an appropriate cumulant generating function and a transform which is closely related to the characteristic function. This leads to a definition of half independent convolution of arbitrary probability measures which is compatible with the distribution of the sum of half independent elements of a noncommutative probability space. We also establish the central limit theorem for half independent convolution of measures with the limit being symmetrized Rayleigh. Cramer's theorem is also established in this set up.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "$C^*$probability space; Central limit theorem; Cramer's theorem; cumulant; free algebras; free independence; half commutativity; half independence; noncommutative probability spaces; Rayleigh distribution; reverse circulant matrix; semicircular law", } @Article{Abramson:2011:CMR, author = "Josh Abramson and Jim Pitman and Nathan Ross and Geronimo Uribe Bravo", title = "Convex minorants of random walks and {L{\'e}vy} processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "38:423--38:434", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1648", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1648", abstract = "This article provides an overview of recent work on descriptions and properties of the Convex minorants of random walks and L{\'e}vy processes, which summarize and extend the literature on these subjects. The results surveyed include point process descriptions of the convex minorant of random walks and L{\'e}vy processes on a fixed finite interval, up to an independent exponential time, and in the infinite horizon case. These descriptions follow from the invariance of these processes under an adequate path transformation. In the case of Brownian motion, we note how further special properties of this process, including time-inversion, imply a sequential description for the convex minorant of the Brownian meander.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random walks, L{\'e}vy processes, Brownian meander, Convex minorant, Uniform stick-breaking, Fluctuation theory", } @Article{Curien:2011:RLM, author = "Nicolas Curien and Yuval Peres", title = "Random laminations and multitype branching processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "39:435--39:446", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1641", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1641", abstract = "We consider multitype branching processes arising in the study of random laminations of the disk. We classify these processes according to their subcritical or supercritical behavior and provide Kolmogorov-type estimates in the critical case corresponding to the random recursive lamination process of [1]. The proofs use the infinite dimensional Perron--Frobenius theory and quasi-stationary distributions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random trees, random snake", } @Article{Liu:2011:EUI, author = "Wei Liu and Jonas Toelle", title = "Existence and Uniqueness of Invariant Measures for Stochastic Evolution Equations with Weakly Dissipative Drifts", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "40:447--40:457", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1643", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1643", abstract = "In this paper, a new decay estimate for a class of stochastic evolution equations with weakly dissipative drifts is established, which directly implies the uniqueness of invariant measures for the corresponding transition semigroups. Moreover, the existence of invariant measures and the convergence rate of corresponding transition semigroup to the invariant measure are also investigated. As applications, the main results are applied to singular stochastic $p$-Laplace equations and stochastic fast diffusion equations, which solves an open problem raised by Barbu and Da Prato in [Stoc. Proc. Appl. 120(2010), 1247-1266].", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "$p$-Laplace equation; dissipative; fast diffusion equation; invariant measure; stochastic evolution equation", } @Article{Groeneboom:2011:TMB, author = "Piet Groeneboom and Nico Temme", title = "The tail of the maximum of {Brownian} motion minus a parabola", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "41:458--41:466", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1645", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1645", abstract = "We analyze the tail behavior of the maximum $N$ of $ \{ W(t) - t^2 : t \ge 0 \} $, where $W$ is standard Brownian motion on $ [0, \infty)$, and give an asymptotic expansion for $ {\mathbb P} \{ N \ge x \} $, as $ x \to \infty $. This extends a first order result on the tail behavior, which can be deduced from H{\"u}sler and Piterbarg (1999). We also point out the relation between certain results in Janson et al. (2010) and Groeneboom (2010).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion, parabolic drift, maximum, Airy functions", } @Article{Nourdin:2011:YAP, author = "Ivan Nourdin", title = "Yet another proof of the {Nualart--Peccati} criterion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "42:467--42:481", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1642", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1642", abstract = "In 2005, Nualart and Peccati showed that, surprisingly, the convergence in distribution of a normalized sequence of multiple Wiener-It{\^o} integrals towards a standard Gaussian law is equivalent to convergence of just the fourth moment to 3. Recently, this result is extended to a sequence of multiple Wigner integrals, in the context of free Brownian motion. The goal of the present paper is to offer an elementary, unifying proof of these two results. The only advanced, needed tool is the product formula for multiple integrals. Apart from this formula, the rest of the proof only relies on soft combinatorial arguments.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion; free Brownian motion; multiple Wiener-It{\^o} integrals; multiple Wigner integrals; Nualart--Peccati criterion; product formula", } @Article{Raimond:2011:IDG, author = "Olivier Raimond and Bruno Schapira", title = "Internal {DLA} generated by cookie random walks on {$Z$}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "43:483--43:490", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1646", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1646", abstract = "We prove a law of large numbers for the right boundary in the model of internal DLA generated by cookie random walks in dimension one. The proof is based on stochastic recursions techniques.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "excited random walk; Internal DLA; law of large numbers.", } @Article{Hasebe:2011:JCN, author = "Takahiro Hasebe and Hayato Saigo", title = "Joint cumulants for natural independence", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "44:491--44:506", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1647", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1647", abstract = "Many kinds of independence have been defined in non-commutative probability theory. Natural independence is an important class of independence; this class consists of five independences (tensor, free, Boolean, monotone and anti-monotone ones). In the present paper, a unified treatment of joint cumulants is introduced for natural independence. The way we define joint cumulants enables us not only to find the monotone joint cumulants but also to give a new characterization of joint cumulants for other kinds of natural independence, i.e., tensor, free and Boolean independences. We also investigate relations between generating functions of moments and monotone cumulants. We find a natural extension of the Muraki formula, which describes the sum of monotone independent random variables, to the multivariate case.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Natural independence, cumulants, non-commutative probability, monotone independence", } @Article{Gripenberg:2011:WCG, author = "Gustaf Gripenberg", title = "White and colored {Gaussian} noises as limits of sums of random dilations and translations of a single function", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "45:507--45:516", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1650", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1650", abstract = "It is shown that a stochastic process obtained by taking random sums of dilations and translations of a given function converges to Gaussian white noise if a dilation parameter grows to infinity and that it converges to Gaussian colored noise if a scaling parameter for the translations grows to infinity. In particular, the question of when one obtains fractional Brownian motion by integrating this colored noise is studied.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion; colored noise; convergence; dilation; fractional Brownian motion; translation; white noise", } @Article{Coupier:2011:MGS, author = "David Coupier", title = "Multiple geodesics with the same direction", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "46:517--46:527", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1656", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1656", abstract = "The directed last-passage percolation (LPP) model with independent exponential times is considered. We complete the study of asymptotic directions of infinite geodesics, started by Ferrari and Pimentel [5]. In particular, using a recent result of [3] and a local modification argument, we prove there is no (random) direction with more than two geodesics with probability 1.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "geodesic; last-passage percolation; random tree; topological end", } @Article{Procaccia:2011:GRI, author = "Eviatar Procaccia and Johan Tykesson", title = "Geometry of the random interlacement", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "47:528--47:544", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1660", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1660", abstract = "We consider the geometry of random interlacements on the $d$-dimensional lattice. We use ideas from stochastic dimension theory developed in [1] to prove the following: Given that two vertices $ x, y$ belong to the interlacement set, it is possible to find a path between $x$ and $y$ contained in the trace left by at most $ \lceil d / 2 \rceil $ trajectories from the underlying Poisson point process. Moreover, this result is sharp in the sense that there are pairs of points in the interlacement set which cannot be connected by a path using the traces of at most $ \lceil d / 2 \rceil - 1$ trajectories.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random Interlacements; Stochastic dimension", } @Article{Bottcher:2011:CFP, author = "Bj{\"o}rn B{\"o}ttcher", title = "On the construction of {Feller} processes with unbounded coefficients", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "48:545--48:555", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1652", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1652", abstract = "Construction methods for Feller processes which require bounded coefficients are extended to the case of unbounded coefficients.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Feller process, Feller semigroup, construction of Markov processes, unbounded coefficients", } @Article{Koudou:2011:WDM, author = "Angelo Koudou and Pierre Vallois", title = "Which distributions have the {Matsumoto--Yor} property?", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "49:556--49:566", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1663", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1663", abstract = "For four types of functions $ \xi :]0, \infty [\to]0, \infty [ $, we characterize the law of two independent and positive r.v.'s $X$ and $Y$ such that $ U := \xi (X + Y)$ and $ V := \xi (X) - \xi (X + Y)$ are independent. The case $ \xi (x) = 1 / x$ has been treated by Letac and Wesolowski (2000). As for the three other cases, under the weak assumption that $X$ and $Y$ have density functions whose logarithm is locally integrable, we prove that the distribution of $ (X, Y)$ is unique. This leads to Kummer, gamma and beta distributions. This improves the result obtained in [1] where more regularity was required from the densities.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Beta distribution.; Gamma distribution; generalized inverse Gaussian distribution; Kummer distribution; Matsumoto--Yor property", } @Article{Mohle:2011:CPD, author = "Martin M{\"o}hle", title = "Coalescent processes derived from some compound {Poisson} population models", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "50:567--50:582", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1654", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1654", abstract = "A particular subclass of compound Poisson population models is analyzed. The models in the domain of attraction of the Kingman coalescent are characterized and it is shown that these models are never in the domain of attraction of any other continuous-time coalescent process. Results are obtained characterizing which of these models are in the domain of attraction of a discrete-time coalescent with simultaneous multiple mergers of ancestral lineages. The results extend those obtained by Huillet and the author in `Population genetics models with skewed fertilities: a forward and backward analysis', Stochastic Models 27 (2011), 521-554.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Ancestral process; Cannings model; coalescent; compound Poisson model; conditional branching process model; Dirichlet model; exchangeability; neutrality; simultaneous multiple collisions; weak convergence; Wright--Fisher model", } @Article{Kuba:2011:ACC, author = "Markus Kuba", title = "Analysis of a class of Cannibal urns", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "51:583--51:599", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1669", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1669", abstract = "In this note we study a class of $ 2 \times 2 $ Polya-Eggenberger urn models, which serves as a stochastic model in biology describing cannibalistic behavior of populations. A special case was studied before by Pittel using asymptotic approximation techniques, and more recently by Hwang et al. using generating functions. We obtain limit laws for the stated class of so-called cannibal urns by using Pittel's method, and also different techniques.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Cannibal Urn models, Normal distribution, Poisson distribution", } @Article{Ma:2011:TII, author = "Yutao Ma and Ran Wang and Liming Wu", title = "Transportation-information inequalities for continuum {Gibbs} measures", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "52:600--52:613", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1670", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1670", abstract = "The objective of this paper is to establish explicit concentration inequalities for the Glauber dynamics related with continuum or discrete Gibbs measures. At first we establish the optimal transportation-information $ W_1 I$-inequality for the $ M / M / \infty $-queue associated with the Poisson measure, which improves several previous known results. Under the Dobrushin's uniqueness condition, we obtain some explicit $ W_1 I$-inequalities for Gibbs measures both in the continuum and in the discrete lattice. Our method is a combination of Lipschitzian spectral gap, the Lyapunov test function approach and the tensorization technique.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "transportation-information inequality, concentration inequality, Gibbs measure, Lyapunov function method", } @Article{Sayit:2011:AFM, author = "Hasanjan Sayit and Frederi Viens", title = "Arbitrage-free Models In Markets With Transaction Costs", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "53:614--53:622", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1671", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1671", abstract = "In the paper [7], Guasoni studies financial markets which are subject to proportional transaction costs. The standard martingale framework of stochastic finance is not applicable in these markets, since the transaction costs force trading strategies to have bounded variation, while continuous- time martingale strategies have infinite transaction cost. The main question that arises out of [7] is whether it is possible to give a convenient condition to guarantee that a trading strategy has no arbitrage. Such a condition was proposed and studied in [6] and [1], the so-called stickiness property, whereby an asset's price is never certain to exit a ball within a predetermined finite time. In this paper, we define the multidimensional extension of the stickiness property, to handle arbitrage-free conditions for markets with multiple assets and proportional transaction costs. We show that this condition is sufficient for a multi-asset model to be free of arbitrage. We also show that d-dimensional fractional Brownian models are jointly sticky, and we establish a time-change result for joint stickiness.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Financial markets, arbitrage, transaction cost, sticky process, fractional Brownian motion, time-change", } @Article{Simon:2011:MSP, author = "Thomas Simon", title = "A multiplicative short proof for the unimodality of stable densities", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "54:623--54:629", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1672", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1672", abstract = "Revisiting an article by Chernin and Ibragimov on unimodality of stable laws, we show that their approach to deduce the general case from the extremal ones, whose completion contained an error as discovered later by Kanter, can be carried out successfully in considering Bochner's subordination and multiplicative strong unimodality. This short proof of the unimodality of all stable densities yields also a multiplicative counterpart to Yamazato's additive ones.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stable law; unimodality", } @Article{Bergqvist:2011:RPR, author = "G{\"o}ran Bergqvist and Peter Forrester", title = "Rank probabilities for real random {$ N \times N \times 2 $} tensors", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "55:630--55:637", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1655", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1655", abstract = "We prove that the probability $ P_N $ for a real random Gaussian $ N \times N \times 2 $ tensor to be of real rank $N$ is $ P_N = (\Gamma ((N + 1) / 2))^N / G(N + 1)$, where $ \Gamma (x)$, $ G(x)$ denote the gamma and Barnes $G$-functions respectively. This is a rational number for $N$ odd and a rational number multiplied by $ \pi^{N / 2}$ for $N$ even. The probability to be of rank $ N + 1$ is $ 1 - P_N$. The proof makes use of recent results on the probability of having $k$ real generalized eigenvalues for real random Gaussian $ N \times N$ matrices. We also prove that $ \log P_N = (N^2 / 4) \log (e / 4) + (\log N - 1) / 12 - \zeta '( - 1) + {\rm O}(1 / N)$ for large $N$, where $ \zeta $ is the Riemann zeta function.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "multi-way arrays; random matrices; tensors; typical rank", } @Article{Jones:2011:CHT, author = "Owen Jones and David Rolls", title = "A characterisation of, and hypothesis test for, continuous local martingales", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "56:638--56:651", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1673", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1673", abstract = "We give characterisations for Brownian motion and continuous local martingales, using the crossing tree, which is a sample-path decomposition based on first-passages at nested scales. These results are based on ideas used in the construction of Brownian motion on the Sierpinski gasket (Barlow and Perkins 1988). Using our characterisation we propose a test for the continuous martingale hypothesis, that is, that a given process is a continuous local martingale. The crossing tree gives a natural break-down of a sample path at different spatial scales, which we use to investigate the scale at which a process looks like a continuous local martingale. Simulation experiments indicate that our test is more powerful than an alternative approach which uses the sample quadratic variation.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "continuous martingale hypothesis; crossing-tree; realised volatility; time-change", } @Article{Markowsky:2011:EET, author = "Greg Markowsky", title = "On the expected exit time of planar {Brownian} motion from simply connected domains", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "57:652--57:663", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1653", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1653", abstract = "In this note, we explore applications of a known lemma which relates the expected exit time of Brownian motion from a simply connected domain with the power series of a conformal map into that domain. We use the lemma to calculate the expected exit time from a number of domains, and in the process describe a probabilistic method for summing certain series. In particular, we give a proof of Euler's classical result that $ \zeta (2) = \pi^2 / 6 $. We also show how the relationship between the power series and the Brownian exit time gives several immediate consequences when teamed with a deep result of de Branges concerning the coefficients of power series of normalized conformal maps. We conclude by stating an extension of the lemma in question to domains which are not simply connected.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Brownian motion; conformal maps; exit time", } @Article{Karatzas:2011:OST, author = "Ioannis Karatzas and Albert Shiryaev and Mykhaylo Shkolnikov", title = "On the one-sided {Tanaka} equation with drift", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "58:664--58:677", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1665", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1665", abstract = "We study questions of existence and uniqueness of weak and strong solutions for a one-sided Tanaka equation with constant drift lambda. We observe a dichotomy in terms of the values of the drift parameter: for $ \lambda \leq 0 $, there exists a strong solution which is pathwise unique, thus also unique in distribution; whereas for $ \lambda > 0 $, the equation has a unique in distribution weak solution, but no strong solution (and not even a weak solution that spends zero time at the origin). We also show that strength and pathwise uniqueness are restored to the equation via suitable ``Brownian perturbations''.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stochastic differential equation, weak existence, weak uniqueness, strong existence, strong uniqueness, Tanaka equation, skew Brownian motion, sticky Brownian motion, comparison theorems for diffusions", } @Article{Dong:2011:IMS, author = "Zhao Dong and Lihu Xu and Xicheng Zhang", title = "Invariant measures of stochastic {$ 2 D $} {Navier--Stokes} equation driven by $ \alpha $-stable processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "59:678--59:688", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1664", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1664", abstract = "In this note we prove the well-posedness for stochastic $ 2 D $ Navier--Stokes equation driven by general L{\'e}vy processes (in particular, $ \alpha $-stable processes), and obtain the existence of invariant measures.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "$alpha$-stable process, Stochastic Navier--Stokes equation, Invariant measure", } @Article{VanNeerven:2011:MIS, author = "Jan {Van Neerven} and Jiahui Zhu", title = "A maximal inequality for stochastic convolutions in $2$-smooth {Banach} spaces", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "60:689--60:705", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1677", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1677", abstract = "Let $ (e^{tA})_{t \geq 0} $ be a $ C_0$-contraction semigroup on a $2$-smooth Banach space $E$, let $ (W_t)_{t \geq 0}$ be a cylindrical Brownian motion in a Hilbert space $H$, and let $ (g_t)_{t \geq 0}$ be a progressively measurable process with values in the space $ \gamma (H, E)$ of all $ \gamma $-Radonifying operators from $H$ to $E$. We prove that for all $ 0 < p < \infty $ there exists a constant $C$, depending only on $p$ and $E$, such that for all $ T \geq 0$ we have\par $$ E \sup_{0 \leq t \leq T} \left \Vert \int_0^t \! e^{(t - s)A} \, g_s d W_s \right \Vert^p \leq C E \left (\int_0^T \! \left (\left \Vert g_t \right \Vert_{\gamma (H, E)} \right)^2 \, d t \right)^{p / 2}. $$ For $ p \geq 2$ the proof is based on the observation that $ \psi (x) = \Vert x \Vert^p$ is Fr{\'e}chet differentiable and its derivative satisfies the Lipschitz estimate $ \Vert \psi '(x) - \psi '(y) \Vert \leq C \left (\Vert x \Vert + \Vert y \Vert \right)^{p - 2} \Vert x - y \Vert $; the extension to $ 0 < p < 2$ proceeds via Lenglart's inequality.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Stochastic convolutions, maximal inequality, $2$-smooth Banach spaces, It{\^o} formula.", } @Article{Sen:2011:ACL, author = "Arnab Sen and Balint Virag", title = "Absolute continuity of the limiting eigenvalue distribution of the random {Toeplitz} matrix", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "61:706--61:711", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1675", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1675", abstract = "We show that the limiting eigenvalue distribution of random symmetric Toeplitz matrices is absolutely continuous with density bounded by 8, partially answering a question of Bryc, Dembo and Jiang (2006). The main tool used in the proof is a spectral averaging technique from the theory of random Schr{\"o}dinger operators. The similar question for Hankel matrices remains open", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Toeplitz matrix, eigenvalue distribution, spectral averaging", } @Article{Quastel:2011:LBP, author = "Jeremy Quastel and Daniel Remenik", title = "Local {Brownian} property of the narrow wedge solution of the {KPZ} equation", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "62:712--62:719", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1678", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1678", abstract = "Abstract. Let $ H(t, x) $ be the Hopf-Cole solution at time t of the Kardar--Parisi--Zhang (KPZ) equation starting with narrow wedge initial condition, i.e. the logarithm of the solution of the multiplicative stochastic heat equation starting from a Dirac delta. Also let $ H^{eq}(t, x) $ be the solution at time $t$ of the KPZ equation with the same noise, but with initial condition given by a standard two-sided Brownian motion, so that $ H^{eq}(t, x) - H^{eq}(0, x)$ is itself distributed as a standard two-sided Brownian motion. We provide a simple proof of the following fact: for fixed $t$, $ H(t, x) - (H^{eq}(t, x) - H^{eq}(t, 0))$ is locally of finite variation. Using the same ideas we also show that if the KPZ equation is started with a two-sided Brownian motion plus a Lipschitz function then the solution stays in this class for all time.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "asymmetric exclusion process; Brownian motion; directed polymers; finite variation; Kardar--Parisi--Zhang equation; random growth; stochastic Burgers equation; stochastic heat equation", } @Article{Pardoux:2011:BML, author = "Etienne Pardoux and Anton Wakolbinger", title = "From {Brownian} motion with a local time drift to {Feller}'s branching diffusion with logistic growth", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "63:720--63:731", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1679", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1679", abstract = "We give a new proof for a Ray-Knight representation of Feller's branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion $H$ with a drift that is affine linear in the local time accumulated by $H$ at its current level. In Le et al. (2011) such a representation was obtained by an approximation through Harris paths that code the genealogies of particle systems. The present proof is purely in terms of stochastic analysis, and is inspired by previous work of Norris, Rogers and Williams (1988).", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Ray-Knight representation, local time, Feller branching with logistic growth, Brownian motion, local time drift, Girsanov transform", } @Article{Fernandez:2011:RMA, author = "Roberto Fernandez and Sandro Gallo and Gregory Maillard", title = "Regular $g$-measures are not always {Gibbsian}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "64:732--64:740", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1681", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1681", abstract = "Regular g-measures are discrete-time processes determined by conditional expectations with respect to the past. One-dimensional Gibbs measures, on the other hand, are fields determined by simultaneous conditioning on past and future. For the Markovian and exponentially continuous cases both theories are known to be equivalent. Its equivalence for more general cases was an open problem. We present a simple example settling this issue in a negative way: there exist $g$-measures that are continuous and non-null but are not Gibbsian. Our example belongs, in fact, to a well-studied family of processes with rather nice attributes: It is a chain with variable-length memory, characterized by the absence of phase coexistence and the existence of a visible renewal scheme", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Discrete-time stochastic processes, $g$-measures, chains with complete connections, non-Gibbsianness, chains with variable-length memory", } @Article{Ramirez:2011:HET, author = "Jose Ramirez and Brian Rider and Ofer Zeitouni", title = "Hard edge tail asymptotics", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "65:741--65:752", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1682", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1682", abstract = "Let $ \Lambda $ be the limiting smallest eigenvalue in the general $ (\beta, a)$-Laguerre ensemble of random matrix theory. That is, $ \Lambda $ is the $ n \to \infty $ distributional limit of the (scaled) minimal point drawn from the density proportional to $ \Pi_1 \leq i \leq j \leq n$ \par $$ \left | \lambda_i - \lambda_j \right |^\beta \prod_{i = 1}^n \lambda_i^{\frac {\beta }{2}(a + 1) - 1}e^{- \frac {\beta }{2} \lambda_i} $$ on $ (\mathbb {R}_+^n$. Here $ \beta > 0$, $ a > - 1$; for $ \beta = 1, 2, 4$ and integer $a$, this object governs the singular values of certain rank $n$ Gaussian matrices. We prove that\par $$ \mathbb {P}(\Lambda > \lambda) = e^{- \frac {\beta }{2} \lambda + 2 \gamma \sqrt {\lambda }} \lambda^{- \frac {\gamma (\gamma + 1 - \beta / 2)}{2 \beta }} e(\beta, a)(1 + o(1)) $$ as $ \lambda \to \infty $ in which\par $$ \gamma = \frac {\beta }{2} (a + 1) - 1 $$ and $ e(\beta, a) > 0$ is a constant (which we do not determine). This estimate complements/extends various results previously available for special values of $ \beta $ and $a$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Random matrices, smallest singular value, hard edge", } @Article{Merkl:2011:CIE, author = "Franz Merkl and Silke Rolles", title = "Correlation Inequalities for Edge-Reinforced Random Walk", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "66:753--66:763", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1683", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1683", abstract = "We prove correlation inequalities for linearly edge-reinforced random walk. These correlation inequalities concern the first entry tree, i.e. the tree of edges used to enter any vertex for the first time. They also involve the asymptotic fraction of time spent on particular edges. Basic ingredients are known FKG-type inequalities and known negative associations for determinantal processes.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "FKG inequalities; reinforced random walk; spanning trees", } @Article{Lejay:2011:SSP, author = "Antoine Lejay", title = "Simulation of a stochastic process in a discontinuous layered medium", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "67:764--67:774", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1686", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1686", abstract = "In this note, we provide a simulation algorithm for a diffusion process in a layered media. Our main tools are the properties of the Skew Brownian motion and a path decomposition technique for simulating occupation times.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Skew Brownian motion, discontinuous media, occupation time, local time, last passage time, path decomposition, Brownian bridge, first hitting time, geophysics, Monte Carlo simulation", } @Article{Sapozhnikov:2011:IIC, author = "Artem Sapozhnikov", title = "The incipient infinite cluster does not stochastically dominate the invasion percolation cluster in two dimensions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "68:775--68:780", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1684", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1684", abstract = "This note is motivated by results of Angel, Goodman, den Hollander and Slade (2008) and Damron, Sapozhnikov and Vagvolgyi (2009) about global relations between the invasion percolation cluster (IPC) and the incipient infinite cluster (IIC) on regular trees and on two dimensional lattices, respectively. Namely, that the laws of the two objects are mutually singular, and, in the case of regular trees, that the IIC stochastically dominates the IPC. We prove that on two dimensional lattices, the IIC does not stochastically dominate the IPC. This is the first example showing that the relation between the IIC and IPC is significantly different on trees and in two dimensions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Invasion percolation, incipient infinite cluster, critical percolation, near-critical percolation, correlation length, stochastic domination.", } @Article{Hutzenthaler:2011:SBD, author = "Martin Hutzenthaler", title = "Supercritical branching diffusions in random environment", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "69:781--69:791", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1685", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1685", abstract = "Supercritical branching processes in constant environment conditioned on eventual extinction are known to be subcritical branching processes. The case of random environment is more subtle. A supercritical branching diffusion in random environment (BDRE) conditioned on eventual extinction of the population is not a branching diffusion in a homogeneous environment. However the law of the population size of a supercritical BDRE (averaged over the environment) conditioned on eventual extinction is equal to the law of the population size of a subcritical BDRE (averaged over the environment). As a consequence, supercritical BDREs have a phase transition which is similar to a well-known phase transition of subcritical branching processes in random environment.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Branching diffusions in random environment, BDRE, supercriticality, survival probability", } @Article{Athreya:2011:ODV, author = "Siva Athreya and Rongfeng Sun", title = "One-dimensional Voter Model Interface Revisited", journal = j-ELECTRON-COMMUN-PROBAB, volume = "16", pages = "70:792--70:800", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v16-1688", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1688", abstract = "We consider the voter model on $ \mathbb {Z} $, starting with all 1's to the left of the origin and all $0$'s to the right of the origin. It is known that if the associated random walk kernel $p$ has zero mean and a finite r-th moment for any $ r > 3$, then the evolution of the boundaries of the interface region between 1's and 0's converge in distribution to a standard Brownian motion $ (B_t)_{t > 0}$ under diffusive scaling of space and time. This convergence fails when $p$ has an infinite $r$-th moment for any $ r < 3$, due to the loss of tightness caused by a few isolated $1$'s appearing deep within the regions of all $0$'s (and vice versa) at exceptional times. In this note, we show that as long as $p$ has a finite second moment, the measure-valued process induced by the rescaled voter model configuration is tight, and converges weakly to the measure-valued process $ 1_{x < B_t} d x$, $ t > 0$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "voter model interface, measure-valued process, tightness", } @Article{Benjamini:2012:RVI, author = "Itai Benjamini and Nicolas Curien", title = "Recurrence of the $ \mathbb {Z}^d$-valued infinite snake via unimodularity", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "1:1--1:10", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1700", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1700", abstract = "We use the concept of unimodular random graph to show that the branching simple random walk on $ \mathbb {Z}^d $ indexed by a critical geometric Galton--Watson tree conditioned to survive is recurrent if and only if $ d \leq 4 $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Galton--Watson trees; random snake; recurrence", } @Article{vandenBerg:2012:PPB, author = "Jacob van den Berg and Demeter Kiss and Pierre Nolin", title = "A percolation process on the binary tree where large finite clusters are frozen", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "2:1--2:11", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1694", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1694", abstract = "We study a percolation process on the planted binary tree, where clusters freeze as soon as they become larger than some fixed parameter N. We show that as N goes to infinity, the process converges in some sense to the frozen percolation process introduced by Aldous. In particular, our results show that the asymptotic behaviour differs substantially from that on the square lattice, on which a similar process has been studied recently by van den Berg, de Lima and Nolin.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "frozen cluster; percolation", } @Article{Freund:2012:ASA, author = "Fabian Freund", title = "Almost sure asymptotics for the number of types for simple {$ \Xi $}-coalescents", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "3:1--3:11", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1704", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1704", abstract = "Let $ K_n $ be the number of types in the sample $ \left \{ 1, \ldots, n \right \} $ of a $ \Xi $-coalescent $ \Pi = (\Pi_t)_{t \geq 0}$ with mutation and mutation rate $ r > 0$. Let $ \Pi^{(n)}$ be the restriction of $ \Pi $ to the sample. It is shown that $ M_n / n$, the fraction of external branches of $ \Pi^{(n)}$ which are affected by at least one mutation, converges almost surely and in $ L^p$ ($ p \geq 1$) to $ M := \int^{\infty }_0 r e^{-rt}S_t d t$, where $ S_t$ is the fraction of singleton blocks of $ \Pi_t$. Since for coalescents without proper frequencies, the effects of mutations on non-external branches is neglectible for the asymptotics of $ K_n / n$, it is shown that $ K_n / n \rightarrow M$ for $ n \rightarrow \infty $ in $ L^p$ $ (p \geq 1)$. For simple coalescents, this convergence is shown to hold almost surely. The almost sure results are based on a combination of the Kingman correspondence for random partitions and strong laws of large numbers for weighted i.i.d. or exchangeable random variables.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "almost sure convergence; coalescent; external branches; mutation", } @Article{Hillion:2012:CEA, author = "Erwan Hillion", title = "Concavity of entropy along binomial convolutions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "4:1--4:9", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1707", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1707", abstract = "Motivated by a generalization of Sturm-Lott-Villani theory to discrete spaces and by a conjecture stated by Shepp and Olkin about the entropy of sums of Bernoulli random variables, we prove the concavity in $t$ of the entropy of the convolution of a probability measure $a$, which has the law of a sum of independent Bernoulli variables, by the binomial measure of parameters $ n \geq 1$ and $t$.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "binomial distribution; concavity of entropy; Olkin-Shepp conjecture", } @Article{Goldberg:2012:CRM, author = "Leslie Goldberg and Mark Jerrum", title = "A counterexample to rapid mixing of the {Ge--Stefankovic} process", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "5:1--5:6", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1712", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1712", abstract = "Ge and Stefankovic have recently introduced a Markov chain which, if rapidly mixing, would provide an efficient procedure for sampling independent sets in a bipartite graph. Such a procedure would be a breakthrough because it would give an efficient randomised algorithm for approximately counting independent sets in a bipartite graph, which would in turn imply the existence of efficient approximation algorithms for a number of significant counting problems whose computational complexity is so far unresolved. Their Markov chain is based on a novel two-variable graph polynomial which, when specialised to a bipartite graph, and evaluated at the point (1/2, 1), gives the number of independent sets in the graph. The Markov chain is promising, in the sense that it overcomes the most obvious barrier to rapid mixing. However, we show here, by exhibiting a sequence of counterexamples, that its mixing timeis exponential in the size of the input when the input is chosen from a particular infinite family of bipartite graphs.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Glauber dynamics; Independent sets in graphs; Markov chains; Mixing time; Randomised algorithms", } @Article{Denisov:2012:MAS, author = "Denis Denisov and Vitali Wachtel", title = "Martingale approach to subexponential asymptotics for random walks", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "6:1--6:9", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1757", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1757", abstract = "Consider the random walk $ S_n = \xi_1 + \cdots + \xi_n $ with independent and identically distributed increments and negative mean $ \mathbf E \xi = - m < 0 $. Let $ M = \sup_{0 \le i} S_i $ be the supremum of the random walk. In this note we present derivation of asymptotics for $ \mathbf P(M > x), x \to \infty $ for long-tailed distributions. This derivation is based on the martingale arguments and does not require any prior knowledge of the theory of long-tailed distributions. In addition the same approach allows to obtain asymptotics for $ \mathbf P(M_\tau > x) $, where $ M_\tau = \max_{0 \le i < \tau }S_i $ and $ \tau = \min \{ n \ge 1 : S_n \le 0 \} $.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "cycle maximum; heavy-tailed distribution; random walk; stopping time; supremum", } @Article{Cator:2012:IIC, author = "Eric Cator and Leandro Pimentel and Marcio Souza", title = "Influence of the initial condition in equilibrium last-passage percolation models", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "7:1--7:7", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1727", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1727", abstract = "In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an $ \mathbb {L}^2$-formula relating the initial measure with the last-passage percolation time. This formula turns out to be a useful tool to analyze the fluctuations of the last-passage times along non-characteristic directions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Equilibrium measure; Hammersley process; Interacting particle system; Last passage percolation", } @Article{Mueller:2012:ECB, author = "Carl Mueller and Zhixin Wu", title = "Erratum: {``A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand''}", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "8:1--8:10", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1774", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", note = "See \cite{Mueller:2009:CBS}.", URL = "http://ecp.ejpecp.org/article/view/1774", abstract = "We give a new representation of fractional Brownian motion with Hurst parameter $ H < 1 / 2 $ using stochastic partial differential equations. This representation allows us to use the Markov property and time reversal, tools which are not usually available for fractional Brownian motion. We then give simple proofs that fractional Brownian motion does not hit points in the critical dimension, and that it does not have double points in the critical dimension. These facts were already known, but our proofs are quite simple and use some ideas of L{\'e}vy. This is an Erratum for \url{https://doi.org/10.1214/ECP.v14-1403}ECP volume 14 paper number 6.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "heat equation; stochastic partial differential equations; white noise", } @Article{Sznitman:2012:ITR, author = "Alain-Sol Sznitman", title = "An isomorphism theorem for random interlacements", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "9:1--9:9", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1792", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1792", abstract = "We consider continuous-time random interlacements on a transient weighted graph. We prove an identity in law relating the field of occupation times of random interlacements at level u to the Gaussian free field on the weighted graph. This identity is closely linked to the generalized second Ray-Knight theorem, and uniquely determines the law of occupation times of random interlacements at level u.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "random interlacements, Gaussian free field, isomorphism theorem, generalized second Ray-Knight theorem.", } @Article{Konig:2012:LDL, author = "Wolfgang K{\"o}nig and Michele Salvi and Tilman Wolff", title = "Large deviations for the local times of a random walk among random conductances", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "10:1--10:11", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1820", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1820", abstract = "We derive an annealed large deviation principle for the normalised local times of a continuous-time random walk among random conductances in a finite domain in $ \mathbb {Z}^d $ in the spirit of Donsker-Varadhan [DV75-83]. We work in the interesting case that the conductances may assume arbitrarily small values. Thus, the underlying picture of the principle is a joint strategy of small values of the conductances and large holding times of the walk. The speed and the rate function of our principle are explicit in terms of the lower tails of the conductance distribution. As an application, we identify the logarithmic asymptotics of the lower tails of the principal eigenvalue of the randomized negative Laplace operator in the domain.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "continuous-time random walk; Donsker-Varadhan rate function; large deviations; random conductances; randomized Laplace operator", } @Article{Arizmendi:2012:PFR, author = "Octavio Arizmendi and Carlos Vargas", title = "Products of free random variables and $k$-divisible non-crossing partitions", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "11:1--11:13", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1773", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1773", abstract = "We derive a formula for the moments and the free cumulants of the multiplication of $k$ free random variables in terms of $k$-equal and $k$-divisible non-crossing partitions. This leads to a new simple proof for the bounds of the right-edge of the support of the free multiplicative convolution $ \mu^{\boxtimes k}$, given by Kargin, which show that the support grows at most linearly with $k$. Moreover, this combinatorial approach generalize the results of Kargin since we do not require the convolved measures to be identical. We also give further applications, such as a new proof of the limit theorem of Sakuma and Yoshida.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "Free multiplicative convolution; Free Probability; Non-crossing partitions", } @Article{Goreac:2012:NLM, author = "Dan Goreac and Oana Silvia Serea", title = "A note on linearization methods and dynamic programming principles for stochastic discontinuous control problems", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "12:1--12:12", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1844", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1844", abstract = "Using the linear programming approach to stochastic control introduced by Buckdahn, Goreac, and Quincampoix, and by Goreac and Serea, we provide a semigroup property for some set of probability measures leading to dynamic programming principles for stochastic control problems. An abstract principle is provided for general bounded costs. Linearized versions are obtained under further (semi)continuity assumptions.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "dynamic programming principles; occupational measures; stochastic control", } @Article{Ejsmont:2012:LLP, author = "Wiktor Ejsmont", title = "{Laha--Lukacs} properties of some free processes", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "13:1--13:8", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1865", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1865", abstract = "We study the Laha--Lukacs property of the free Meixner laws (processes). We prove that some families of free Meixner distribution have the linear regression function. We also show that this families have the property of quadratic conditional variances.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", keywords = "conditional expectation; free cumulants; Free Meixner law; Laha--Lukacs theorem; noncommutative quadratic regression; von Neumann algebras.", } @Article{Hsu:2012:TIS, author = "Daniel Hsu and Sham Kakade and Tong Zhang", title = "Tail inequalities for sums of random matrices that depend on the intrinsic dimension", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "14:1--14:13", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1869", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1869", abstract = "This work provides exponential tail inequalities for sums of random matrices that depend only on intrinsic dimensions rather than explicit matrix dimensions. These tail inequalities are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the explicit dimensions are large or infinite. Some applications to covariance estimation and approximate matrix multiplication are given to illustrate the utility of the new bounds.", acknowledgement = ack-nhfb, ajournal = "Electron. Commun. Probab.", fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Cammarota:2012:MVS, author = "Valentina Cammarota and Peter M{\"o}rters", title = "On the most visited sites of planar {Brownian} motion", journal = j-ELECTRON-COMMUN-PROBAB, volume = "17", pages = "15:1--15:9", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/ECP.v17-1809", ISSN = "1083-589X", ISSN-L = "1083-589X", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/ecp.bib", URL = "http://ecp.ejpecp.org/article/view/1809", abstract = "Let $ (B_t \colon t \ge 0) $ be a planar Brownian motion and de