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作者：Narayanan, Hariharan; Rajaraman, Amit; Srivastava, Piyush
作者单位：Tata Institute of Fundamental Research (TIFR); Massachusetts Institute of Technology (MIT)
摘要：A standard approach for sampling approximately uniformly from a convex body K subset of Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K \subseteq \mathbb {R}<^>n$$\end{document} is to run a random walk within K. The requirement is that starting from a suitable initial distribution, the random walk should mix ra...
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作者：Hong, Wei; Li, Shihu; Liu, Wei
作者单位：Jiangsu Normal University
摘要：In this paper, we provide a general framework for investigating McKean-Vlasov stochastic partial differential equations. We first show the existence of weak solutions by combining the localizing approximation, Faedo-Galerkin technique, compactness method and the Jakubowski version of the Skorokhod representation theorem. Then under certain locally monotone condition we further investigate the existence and uniqueness of (probabilistically) strong solutions. The applications of the main results...
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作者：Lehmkuehler, Matthis; Qian, Wei; Werner, Wendelin
作者单位：University of Basel; University of Hong Kong; University of Cambridge
摘要：The critical two-dimensional Brownian loop-soup is an infinite collection of non-interacting Brownian loops in a planar domain that possesses some combinatorial features related to the notion of indistinguishability of bosons. The properly renormalized occupation time field of this collection of loops is known to be distributed like the properly defined square of a Gaussian free field. In the present paper, we study how much information these fields provide about the loop-soup. Among other thi...
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作者：Husson, Jonathan; Ko, Justin
作者单位：University of Michigan System; University of Michigan; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We consider the asymptotics of rank k spherical integrals when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k = o(N)$$\end{document}. We prove that the sublinear rank spherical integrals are approximately the products of rank 1 spherical integrals. Our formulas extend the results for rank k spherical integrals p...
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作者：Fang, Xiao; Liu, Song-Hao; Shao, Qi-Man; Zhao, Yi-Kun
作者单位：Chinese University of Hong Kong; Dalian University of Technology; Southern University of Science & Technology; Southern University of Science & Technology
摘要：The question of whether the central limit theorem (CLT) holds for the total number of edges in exponential random graph models (ERGMs) in the subcritical region of parameters has remained an open problem. In this paper, we establish the CLT. As a result of our proof, we also derive a convergence rate for the CLT, an explicit formula for the asymptotic variance, and the CLT for general subgraph counts. To establish our main result, we develop Stein's method for the normal approximation of gener...
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作者：Cannizzaro, G.; Goncalves, P.; Misturini, R.; Occelli, A.
作者单位：University of Warwick; Universidade de Lisboa; Universidade Federal do Rio Grande do Sul; Universite d'Angers
摘要：We study the equilibrium fluctuations of an interacting particle system evolving on the discrete ring with N is an element of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\in {\mathbb {N}}$$\end{document} points, denoted by TN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{a...
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作者：Dembin, Barbara; Severo, Franco
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
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...
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作者：Grazieschik, P.; Matetski, K.; Weber, H.
作者单位：University of Bath; Michigan State University; University of Munster
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作者：Maltsev, Anna; Osman, Mohammed
作者单位：University of London; Queen Mary University London
摘要：We consider NxN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\times N$$\end{document} matrices with complex entries that are perturbed by a complex Gaussian matrix with small variance. We prove that if the unperturbed matrix satisfies certain local laws then the bulk correlation functions are universal in the la...
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作者：Grube, Sebastian
作者单位：University of Bielefeld
摘要：While the nondegenerate case is well known, there are only few results on the existence of strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type in the degenerate case. We consider a broad class of degenerate nonlinear Fokker-Planck(-Kolmogorov) equations with coefficients of Nemytskii-type. This includes, in particular, the classical porous medium equation perturbed by a first-order term with initial datum in a subset of probability densities, which is dense with respect ...
