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作者：Banerjee, Sayan; Budhiraja, Amarjit; Imon, Dilshad
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：We study a pure-jump n-particle system with attractive mean field interactions under which each particle jumps forward by a random amount, independently sampled from a given distribution theta , at exponentially distributed times with rate given by a function w of its signed distance from the system center of mass. The function w is taken to be non-increasing which leads to a 'flocking' behavior: the particles below the center of mass jump forward at a higher rate than those above it. This mod...
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作者：Kawamoto, Yosuke
作者单位：Okayama University
摘要：We consider an infinite system of interacting Brownian motions that preserves a given random point field invariant. Such dynamics are constructed using Dirichlet form theory, which naturally leads to two Dirichlet forms for the random point field: the upper and the lower Dirichlet forms. A fundamental question is the uniqueness of the Dirichlet form: that is, whether these two forms coincide. This uniqueness has often been imposed as a key assumption in the Dirichlet form approach to the stoch...
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作者：[Anonymous]
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作者：Dareiotis, Konstantinos; Holland, Teodor; Le, Khoa
作者单位：University of Leeds
摘要：We consider the stochastic reaction-diffusion equation in 1+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+1$$\end{document} dimensions driven by multiplicative space-time white noise, with a distributional drift belonging to a Besov-H & ouml;lder space with any regularity index strictly larger than -1\document...
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作者：Jirak, Moritz; Minsker, Stanislav; Shen, Yiqiu; Wahl, Martin
作者单位：University of Vienna; University of Southern California; University of Southern California; University of Bielefeld
摘要：We prove Fuk-Nagaev and Rosenthal-type inequalities for sums of independent random matrices, focusing on the situation when the norms of the matrices possess finite moments of only low orders. Our bounds depend on the intrinsic dimensional characteristics such as the effective rank, as opposed to the dimension of the ambient space. We illustrate the advantages of such results through several applications, including new moment inequalities for sample covariance matrices and their eigenvectors w...
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作者：Archer, Eleanor; Hartarsky, Ivailo; Kolesnik, Brett; Olesker-Taylor, Sam; Schapira, Bruno; Valesin, Daniel
作者单位：Technische Universitat Wien; University of Warwick; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In Catalan percolation, all nearest-neighbour edges {i, i + 1} along Z are initially occupied, and all other edges are open independently with probability p. Open edges {i, j} are occupied if some pair of edges {i, k} and {k, j}, with i < k < j, become occupied. This model was introduced by Gravner and the third author, in the context of polluted graph bootstrap percolation. We prove that the critical pc is strictly between that of oriented site percolation on Z(2) and the Catalan growth rate ...
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作者：Gu, Chenlin; Su, Zhonggen; Xu, Ruizhe
作者单位：Tsinghua University; Zhejiang University
摘要：For the supercritical Bernoulli bond percolation on \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} (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setl...
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作者：Benard, Timothee; Breuillard, Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); University of Oxford
摘要：We establish the (non-lattice) local limit theorem for products of i.i.d. random variables on an arbitrary simply connected nilpotent Lie group G, where the variables are allowed to be non-centered. Our result also improves on the known centered case by proving uniformity for two-sided moderate deviations and allowing measures with a moment of order 2(dimG)2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \us...
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作者：Haslegrave, John; Keevash, Peter
作者单位：Lancaster University; University of Oxford
摘要：We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet. We study the equilibrium time of the process, by which we mean the number of steps taken until no further interactions can occur. Under a rather general framework, we obtain high probability upper and lower bounds on the equilibrium time that match up to a c...
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作者：Arizmendi, Octavio; Hasebe, Takahiro; Kitagawa, Yu
作者单位：CIMAT - Centro de Investigacion en Matematicas; Hokkaido University; Kyoto University
摘要：We develop analytic tools for studying the free multiplicative convolution of any measure on the real line and any measure on the nonnegative real line. More precisely, we construct the subordination functions and the S-transform of an arbitrary probability measure. The important multiplicativity of S-transform is proved with the help of subordination functions. We then apply the S-transform to establish convolution identities for stable laws, which had been considered in the literature only f...
