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作者：Ding, Jian; Yang, Peng; Zhuang, Zijie
作者单位：Peking University; University of Pennsylvania
摘要：In this paper, we study the evolution of the zero-temperature random field Ising model as the mean of the external field M increases from -infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\infty $$\end{document} to infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{a...
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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：Chaintron, Louis-Pierre; Conforti, Giovanni
作者单位：Universite PSL; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure (ENS); Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria; University of Padua
摘要：We consider a system of diffusion processes interacting through their empirical distribution. Assuming that the empirical average of a given observable can be observed at any time, we derive regularity and quantitative stability results for the optimal solutions in the associated version of the Gibbs conditioning principle. The proofs rely on the analysis of a McKean-Vlasov control problem with distributional constraints. Some new estimates are derived for Hamilton-Jacobi-Bellman equations and...
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作者：Hutchcroft, Tom
作者单位：California Institute of Technology
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作者：Chen, Hong-Bin; Xia, Jiaming
作者单位：New York University; University of Pennsylvania
摘要：We give a meaning to the Hamilton-Jacobi equation arising from mean-field spin glass models in the viscosity sense, and establish the corresponding well-posedness. Originally defined on the set of monotone probability measures, these equations can be interpreted, via an isometry, to be defined on an infinite-dimensional closed convex cone with an empty interior in a Hilbert space. We prove the comparison principle, and the convergence of finite-dimensional approximations furnishing the existen...
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作者：Jiao, Yong; Osekowski, Adam; Wu, Lian
作者单位：Central South University; University of Warsaw
摘要：We introduce the notion of differential subordination in the context of noncommutative continuous-time martingales and show that for 2 < infinity this domination enforces the corresponding L-p bound between the two processes. As applications, we obtain best-order L-p inequalities for the second-order Riesz transforms on a class of group von Neumann algebras equipped with a conditionally negative length function. The proof relies on a novel stochastic representation of these second-order operat...
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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 ...
