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作者：Bass, Richard F.; Burdzy, Krzysztof
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：Consider the deterministic Skorokhod equation in the closed first quadrant: X-t=x(0)+f(t)+integral(t)(0)v(X-s)dL(s), where f:[0,infinity)-> R-2 is a continuous function, f(0)=0, X-t takes values in the quadrant for all t, and L-t is a process that starts at 0, is non-decreasing and continuous, and increases only at those times when is on the boundary of the quadrant. Suppose v on the positive x axis, equals (1,-a(2)) on the positive y axis, and v(0) points into the closed first quadrant. Let t...
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作者：Bass, Richard F.; Burdzy, Krzysztof
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：Consider the deterministic Skorokhod equation in the closed first quadrant: X-t=x(0)+f(t)+integral(t)(0)v(X-s)dL(s), where f:[0,infinity)-> R-2 is a continuous function, f(0)=0, X-t takes values in the quadrant for all t, and L-t is a process that starts at 0, is non-decreasing and continuous, and increases only at those times when is on the boundary of the quadrant. Suppose v on the positive x axis, equals (1,-a(2)) on the positive y axis, and v(0) points into the closed first quadrant. Let t...
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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：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：Prevost, Alexis; Rodriguez, Pierre-Francois; Sousi, Perla
作者单位：University of Bonn; Imperial College London; University of Cambridge
摘要：Let X be a random walk on the torus of side length N in dimension d >= 3 with uniform starting point, and t(cov) be the expected value of its cover time, which is the first time that X has visited every vertex of the torus at least once. For alpha> 0, the set L-alpha of alpha-late points consists of those points not visited by X at time alpha t(cov). We prove the existence of a value alpha & lowast; is an element of ( 1/2 , 1) across which L-alpha trivialises as follows: for all alpha>alpha & ...
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作者：Sojmark, Andreas; Wunderlich, Fabrice
作者单位：University of London; London School Economics & Political Science; University of Oxford
摘要：We provide criteria for It & ocirc; integration to behave continuously with respect to Skorokhod's J1 and M1 topologies, when the integrands and integrators converge weakly or in probability. The results are novel in the M1 setting and unify existing theories in the J1 case. Beyond sufficient criteria, we present an example of uniformly convergent martingale integrators for which the continuity breaks down. Moreover, we show that, for families of local martingales, M1 tightness in fact implies...
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作者：Bernou, Armand; Duerinckx, Mitia
作者单位：Universite Lyon 1; Universite Libre de Bruxelles
摘要：We consider a system of N classical Brownian particles interacting via a smooth long-range potential in the mean-field regime, and we analyze the propagation of chaos in form of uniform-in-time estimates with optimal N-dependence on many-particle correlation functions. Our results cover both the kinetic Langevin setting and the corresponding overdamped Brownian dynamics. The approach is mainly based on so-called Lions expansions, which we combine with new diagrammatic tools to capture many-par...
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作者：Melbourne, James; Nayar, Piotr; Roberto, Cyril
作者单位：CIMAT - Centro de Investigacion en Matematicas; University of Warsaw; Centre National de la Recherche Scientifique (CNRS)
摘要：We show that for log-concave real random variables with fixed variance the Shannon differential entropy is minimized for an exponential random variable, answering a 2010 question of Bobkov and Madiman [1]. This gives a sharp reversal of the celebrated entropy maximization theorem due to Boltzmann, in the log-concave case. We apply this result to derive upper bounds on capacities of additive noise channels with log-concave noise. We also improve constants in the reverse entropy power inequaliti...
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作者：Schmid, Dominik; Sly, Allan
作者单位：University of Augsburg; Princeton University
摘要：We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a circle of length N with k particles. We show that the mixing time is of order N2min(k,N-k)-1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N<^>{2}\min (k,N-k)<^>{-1/2}$$\end{document}, and that the cutoff phenomenon does not o...
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作者：Panis, Romain
作者单位：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 consider the critical FK-Ising measure phi beta c on Z(d) with d >= 3. We construct the measure phi infinity:=lim|x|->infinity phi beta c[|0 <--> x] and prove it satisfies phi infinity[0 <-->infinity]=1. This corresponds to the natural candidate for the incipient infinite cluster measure of the FK-Ising model. Our proof uses a result of Lupu and Werner (Electron. Commun. Probab., 2016) that relates the FK-Ising model to the random current representation of the Ising model, together with a m...
