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作者：Osman, Mohammed
作者单位：University of London; Queen Mary University London
摘要：We prove that the local eigenvalue statistics in the bulk for complex random matrices with independent entries whose r-th absolute moment decays as N-1-(r-2)& varepsilon; for some & varepsilon;>0 are universal. This includes sparse matrices whose entries are the product of a Bernouilli random variable with mean N-1+& varepsilon; and an independent complex-valued random variable. By a standard truncation argument, we can also conclude universality for complex random matrices with 4+& varepsilon...
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作者：Angel, Omer; Senizergues, Delphin
作者单位：University of British Columbia; Centre National de la Recherche Scientifique (CNRS)
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作者：Chen, Xinxin; Lin, Shen
作者单位：Beijing Normal University; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
摘要：We study the critical branching random walk on Zd started from a distant point x and conditioned to hit some compact set K in Zd . We are interested in the occupation time in K and present its asymptotic behaviors in different dimensions. It is shown in this work that the occupation time is of order & Vert;x & Vert;4-d in dimensions d <= 3 , of order log & Vert;x & Vert; in dimension d=4 , and of order 1 in dimensions d >= 5 . The corresponding weak convergences are also established. These res...
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作者：Higgs, Frankie
作者单位：University of Bath
摘要：We analyse the aggregate Loewner evolution (ALE), introduced in 2018 by Sola, Turner and Viklund to generalise versions of diffusion limited aggregation (DLA) in the plane using complex analysis. They showed convergence of the ALE for certain parameters to a single growing slit. Started from a non-trivial initial configuration of k needles and the same parameters, we show that the small-particle scaling limit of ALE is the Laplacian path model, introduced by Carleson and Makarov, in which the ...
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作者：Foondun, Mohammud; Khoshnevisan, Davar; Nualart, Eulalia
作者单位：University of Strathclyde; Utah System of Higher Education; University of Utah; Pompeu Fabra University; Barcelona School of Economics
摘要：We consider a parabolic stochastic partial differential equation (SPDE) on [0, 1] that is forced with multiplicative space-time white noise with a bounded and Lipschitz diffusion coefficient and a drift coefficient that is locally Lipschitz and satisfies an LlogL growth condition. We prove that the SPDE is well posed when the initial data is in L-2[0,1]. This solves a strong form of an open problem.
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作者：Galicza, Pal; Pete, Gabor
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Budapest University of Technology & Economics
摘要：For a sequence of Boolean functions fn:{-1,1}Vn ->{-1,1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_n : \{-1,1\}<^>{V_n} \longrightarrow \{-1,1\}$$\end{document}, with random input given by some probability measure Pn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}...
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作者：Chu, Raymond; Kim, Inwon; Kim, Young-Heon; Nam, Kyeongsik
作者单位：University of California System; University of California Los Angeles; University of British Columbia; Korea Advanced Institute of Science & Technology (KAIST)
摘要：We study the nonlocal Stefan problem, where the phase transition is described by a nonlocal diffusion as well as the change of enthalpy functions. By using a stochastic optimization approach introduced in Kim and Kim (The Stefan problem and free targets of optimal Brownian martingale transport, 2021. arXiv preprint arXiv:2110.03831), we construct global-time weak solutions and give a probabilistic interpretation for the solutions. An important ingredient in our analysis is a probabilistic inte...
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作者：van den Berg, Jacob; Nolin, Pierre
作者单位：Centrum Wiskunde & Informatica (CWI); City University of Hong Kong
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作者：Chiusole, Gideon; Friz, Peter K.
作者单位：Technical University of Munich; Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Wiener spaces are in many ways the decisive setting for fundamental results on Gaussian measures: large deviations (Schilder), quasi-invariance (Cameron-Martin), differential calculus (Malliavin), support description (Stroock-Varadhan), concentration of measure (Fernique), ...Analogues of these classical results have been derived in the enhanced context of Gaussian rough paths and, more recently, regularity structures equipped with Gaussian models. The aim of this article is to propose a simil...
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作者：Dembin, Barbara; Severo, Franco
作者单位：Universites de Strasbourg Etablissements Associes; Centre National de la Recherche Scientifique (CNRS); Universite de Strasbourg; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; 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 prove that the supercritical phase of Voronoi percolation on R-d, d >= 3, is well behaved in the sense that for every p>p(c)(d) local uniqueness of macroscopic clusters happens with high probability. As a consequence, truncated connection probabilities decay exponentially fast and percolation happens on sufficiently thick 2D slabs. This is the analogue of the celebrated result of Grimmett and Marstrand for Bernoulli percolation and serves as the starting point for renormalization techniques...
