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作者：Forsstrom, Malin P.; Gantert, Nina; Steif, Jeffrey E.
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：Motivated by Alain-Sol Sznitman's interlacement process, we consider the set of {0,1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{0,1\}$$\end{document}-valued processes which can be constructed in an analogous way, namely as a union of sets coming from a Poisson process on a collection of sets. Our main focus ...
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作者：Dembo, Amir; Subag, Eliran
作者单位：Stanford University; Weizmann Institute of Science
摘要：We study the law of a random field fN(sigma) evaluated at a random sample from the Gibbs measure associated to a Gaussian field HN(sigma) . In the high-temperature regime, we show that bounds on the probability that fN(sigma)is an element of A for sigma randomly sampled from the Gibbs measure can be deduced from similar bounds for deterministic sigma under the conditional Gaussian law given that HN(sigma)/N=E for E close to the derivative F '(beta) of the free energy (which is the typical valu...
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作者：Fevrier, Maxime; Nica, Alexandru; Szpojankowski, Kamil
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); University of Waterloo; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Warsaw University of Technology
摘要：We study the problem of free denoising. For free selfadjoint random variables a, b, where we interpret a as a signal and b as noise, we find E(a|a+b)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ E (a \, | \, a+b)$$\end{document}. To that end, we study a probability measure mu a,a+b(ov)\documentclass[12pt]{minima...
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作者：Gu, Chenlin; Su, Zhonggen; Xu, Ruizhe
作者单位：Tsinghua University; Zhejiang University
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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 ...
