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作者：Funaki, Tadahisa
摘要：We consider the Glauber-Kawasaki dynamics on a d-dimensional periodic lattice of size N, that is, a stochastic time evolution of particles performing random walks with interaction subject to the exclusion rule (Kawasaki part), in general, of non-gradient type, together with the effect of the creation and annihilation of particles (Glauber part) whose rates are set to favor two levels of particle density, called sparse and dense. We then study the limit of our dynamics under the hydrodynamic sp...
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作者：Schmid, Dominik; Sly, Allan
作者单位：University of Augsburg; Princeton University
摘要：We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a circle of length N with k particles. We show that the mixing time is of order N2min(k,N-k)-1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N<^>{2}\min (k,N-k)<^>{-1/2}$$\end{document}, and that the cutoff phenomenon does not o...
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作者：Panis, Romain
作者单位：Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider the critical FK-Ising measure phi beta c on Z(d) with d >= 3. We construct the measure phi infinity:=lim|x|->infinity phi beta c[|0 <--> x] and prove it satisfies phi infinity[0 <-->infinity]=1. This corresponds to the natural candidate for the incipient infinite cluster measure of the FK-Ising model. Our proof uses a result of Lupu and Werner (Electron. Commun. Probab., 2016) that relates the FK-Ising model to the random current representation of the Ising model, together with a m...
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作者：Biskup, Marek
作者单位：University of California System; University of California Los Angeles
摘要：We study the asymptotic distribution of random walks on Zd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb Z<^>d$$\end{document} (d >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgr...
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作者：Gu, Haotian; Zhang, Zhenyuan
作者单位：University of California System; University of California Los Angeles; Stanford University
摘要：We investigate the low moments E[|A(N) |(2q)], 0 < q <= 1 of secular coefficients A(N) of the critical non-Gaussian holomorphic multiplicative chaos, i.e. coefficients of zN in the power series expansion of exp(Sigma(infinity)(k = 1) X-k z(k)/ root k), where {X-k} (k >= 1) are i.i.d. rotationally invariant unit variance complex random variables. Inspired by Harper's remarkable result on random multiplicative functions, Soundararajan and Zaman recently showed that if each X-k is standard comple...
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作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We consider the area of spheres centered at the distinguished point in the Brownian plane. As a function of the radius, the resulting process has continuously differentiable sample paths. Furthermore, the pair consisting of the process and its derivative is time-homogeneous Markov and satisfies an explicit stochastic differential equation.
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作者：Champagnat, Nicolas; Strickler, Edouard; Villemonais, Denis
作者单位：Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Lorraine; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Institut Universitaire de France
摘要：For general penalized Markov processes with soft killing, we propose a simple criterion ensuring uniform convergence of conditional distributions in Wasserstein distance to a unique quasi-stationary distribution. We give several examples of application where our criterion can be checked, including Bernoulli convolutions and piecewise deterministic Markov processes of the form of switched dynamical systems, for which convergence in total variation is not possible.
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作者：Riabov, Volodymyr
作者单位：Institute of Science & Technology - Austria
摘要：We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear eigenvalue statistics at the cusp-like singularities were not studied in any ensemble. Our analysis covers not only the exact cusps but the entire transitionary regime from the square-root singularity at a regular edge through the sharp cusp to the bulk. We ide...
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作者：Koike, Yuta
作者单位：University of Tokyo; Japan Science & Technology Agency (JST)
摘要：The recent seminal work of Chernozhukov, Chetverikov and Kato has shown that bootstrap approximation for the maximum of a sum of independent random vectors is justified even when the dimension is much larger than the sample size. In this context, numerical experiments suggest that third-moment matching bootstrap approximations would outperform normal approximation even without studentization, but the existing theoretical results cannot explain this phenomenon. In this paper, we develop an asym...
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作者：Bartl, Daniel; Mendelson, Shahar
作者单位：National University of Singapore; National University of Singapore; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We show that under minimal assumptions on a class of functions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {H}$$\end{document} defined on a probability space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackag...
