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作者：Van Werde, Alexander; Sanders, Jaron
作者单位：Eindhoven University of Technology; University of Munster
摘要：We prove that a sum of random matrices generated by a psi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-mixing Markov chain has similar spectral properties to a Gaussian matrix with the same mean and covariance structure. This nonasymptotic universality principle enables sharp concentration i...
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作者：Otto, Felix; Palmieri, Matteo; Wagner, Christian
作者单位：Max Planck Society; Institute of Science & Technology - Austria
摘要：We study a (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}-dimensional semi-discrete random variational problem that can be interpreted as the geometrically linearized version of the critical 2-dimensional random field Ising model. The scaling of the correlation length of the latter was r...
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作者：Bernardin, Cedric; Chhaibi, Reda; Najnudel, Joseph; Pellegrini, Clement
作者单位：HSE University (National Research University Higher School of Economics); Communaute d'universites et etablissements de Toulouse (Comue); Universite de Toulouse (EPE); Centre National de la Recherche Scientifique (CNRS); Institut National des Sciences Appliquees de Toulouse; CNRS - National Institute for Mathematical Sciences (INSMI); University of Bristol
摘要：We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347-369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of the authors show the appearance of spikes in the filtered process, akin to a metastability phenomenon. This paper is aimed at understanding the ...
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作者：Choi, Inhyeok
作者单位：Korea Institute for Advanced Study (KIAS)
摘要：Let G be a countable group whose action on a metric space X involves a contracting isometry. This setting naturally encompasses groups acting on Gromov hyperbolic spaces, Teichm & uuml;ller space, Culler-Vogtmann Outer space and CAT(0) spaces. We discuss continuity and differentiability of the escape rate of random walks on G. For relatively hyperbolic groups, CAT(-1) groups and CAT(0) cubical groups, we further discuss analyticity of the escape rate. Finally, assuming that the action of G on ...
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作者：Cannizzaro, Giuseppe; Giles, Harry
作者单位：University of Warwick
摘要：We investigate the large-scale behaviour of the Self-Repelling Brownian Polymer (SRBP) in the critical dimension d=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=2$$\end{document}. The SRBP is a model of self-repelling motion, which is formally given by the solution to a stochastic differential equation driven ...
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作者：Doeblin, Wolfgang
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作者：Lambert, Gaultier; Najnudel, Joseph
作者单位：Royal Institute of Technology; University of Bristol
摘要：The goal of this article is to expand on the relationship between random matrix and multiplicative chaos theories using the integrability properties of the circular beta-ensembles. We obtain the multiplicative chaos convergence for the characteristic polynomial and eigenvalue counting function of the circular beta-ensembles throughout the subcritical phase, including negative powers. This generalizes recent results in the unitary case, [8, 40], to any beta > 0} and for the eigenvalue counting ...
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作者：Butori, Federico; Flandoli, Franco; Luongo, Eliseo; Tahraoui, Yassine
作者单位：Scuola Normale Superiore di Pisa; University of Bielefeld
摘要：In the last few years it was proved that scalar passive quantities subject to suitable stochastic transport noise, and more recently that also vector passive quantities subject to suitable stochastic transport and stretching noise, weakly converge to the solutions of deterministic equations with a diffusion term. In the background of these stochastic models, we introduce stochastic Vlasov equations which give additional information on the fluctuations and oscillations of solutions: we prove co...
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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：Duminil-Copin, Hugo; Panis, Romain
作者单位：Universite Paris Saclay; University of Geneva; Centre National de la Recherche Scientifique (CNRS); Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Jean Monnet; Universite Lyon 1; Ecole Centrale de Lyon
