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作者：Boursier, Jeanne; Chafai, Djalil; Labbe, Cyril
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite
摘要：We study the Dyson-Ornstein-Uhlenbeck diffusion process, an evolving gas of interacting particles. Its invariant law is the beta Hermite ensemble of random matrix theory, a non-product log-concave distribution. We explore the convergence to equilibrium of this process for various distances or divergences, including total variation, relative entropy, and transportation cost. When the number of particles is sent to infinity, we show that a cutoff phenomenon occurs: the distance to equilibrium va...
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作者：Cardot, Herve; Mas, Andre; Sarda, Pascal
作者单位：Institut Agro; AgroSup Dijon; Universite de Montpellier; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Toulouse; Universite de Toulouse - Jean Jaures
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作者：Dinh, Tien-Cuong; Kaufmann, Lucas; Wu, Hao
作者单位：National University of Singapore; Institute for Basic Science - Korea (IBS); Centre National de la Recherche Scientifique (CNRS); Universite de Orleans
摘要：We obtain various new limit theorems for random walks on SL2(C) under low moment conditions. For non-elementary measures with a finite second moment we prove a Local Limit Theorem for the norm cocycle, yielding the optimal version of a theorem of E. Le Page. For measures with a finite third moment, we obtain the Local Limit Theorem for the matrix coefficients, improving a recent result of Grama-Quint-Xiao and the authors, and Berry-Esseen bounds with optimal rate O(1/root n) for the norm cocyc...
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作者：Hayakawa, Satoshi; Lyons, Terry; Oberhauser, Harald
作者单位：University of Oxford
摘要：For a d-dimensional random vector X, let p(n,X)(theta) be the probability that the convex hull of n independent copies of X contains a given point theta. We provide several sharp inequalities regarding p(n,X)(theta) and N-X(theta) denoting the smallest n for which p(n,X)(theta) >= 1/2. As a main result, we derive the totally general inequality 1/2 <= alpha(X)(theta)N-X(theta) <= 3d + 1, where alpha(X)(theta) (a.k.a. the Tukey depth) is the minimum probability that X is in a fixed closed halfsp...
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作者：Croydon, D. A.; Shiraishi, D.
作者单位：Kyoto University
摘要：We correct a proof in the article 'D. Shiraishi, Exact value of the resistance exponent for four dimensional random walk trace, Probab. Theory and Related Fields 153 (2012), no. 1-2, 191-232'.
