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作者：Ren, Zhenjie; Wang, Songbo
作者单位：Universite Cote d'Azur
摘要：We investigate Gibbs measures for diffusive particles interacting through a two-body mean field energy. By identifying a gradient structure for the conditional law, we derive sharp bounds on the size of chaos, providing a quantitative characterization of particle independence. To handle interaction forces that are unbounded at infinity, we study the concentration of measure phenomenon for Gibbs measures via a defective Talagrand inequality, which may hold independent interest. Our approach pro...
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作者：Bernou, Armand; Duerinckx, Mitia
作者单位：Universite Claude Bernard 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：Baxendale, Peter H.
作者单位：University of Southern California
摘要：This paper considers the effect of additive white noise on the normal form for the supercritical Hopf bifurcation in 2 dimensions. The main results involve the asymptotic behavior of the top Lyapunov exponent lambda associated with this random dynamical system as one or more of the parameters in the system tend to 0 or infinity. This enablesthe construction of a bifurcation diagram in parameter space showing stable regionswhere lambda<0 (implying synchronization) and unstable regions where lam...
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作者：Ren, Panpan; Wang, Feng-Yu
作者单位：Tianjin University; City University of Hong Kong
摘要：By developing a new technique called the bi-coupling argument, we estimate the relative entropy between different diffusion processes in terms of the distances of initial distributions and drift-diffusion coefficients. As an application, the entropy-cost inequality is established for McKean-Vlasov SDEs with spatial-distribution dependent noise, which is open for a long time and has potential applications in optimal transport, information theory and mean field particle systems.
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作者：Devlin, Charles
作者单位：University of Chicago
摘要：Liouville first passage percolation (LFPP) with parameter xi > 0 is the family of random distance functions (metrics) (D-h(is an element of))is an element of > 0 on obtained heuristically by integrating e(xi h) along paths, where h is a variant of the Gaussian free field. There is a critical value xi(crit )approximate to 0.41 such that for xi is an element of (0, xi(crit)), appropriately rescaled LFPP converges in probability uniformly on compact subsets of C to a limiting metric D-h on gamma-...
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作者：Osada, Hirofumi
作者单位：Chubu University
摘要：We prove that the tagged particles of infinitely many Brownian particles in R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\mathbb {R}} <^>2$$\end{document} interacting via a logarithmic (two-dimensional Coulomb) potential with inverse temperature beta=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepa...
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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：Dolgopyat, Dmitry; Hafouta, Yeor
作者单位：University System of Maryland; University of Maryland College Park; State University System of Florida; University of Florida
摘要：We prove Berry-Esseen theorems for sums Sn=& sum;j=0n-1fj degrees Tj-1 degrees & ctdot;degrees T1 degrees T0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ S_n=\sum _{j=0}<^>{n-1}f_j\circ T_{j-1}\circ \cdots \circ T_1\circ T_0$$\end{document} where fj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{w...
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作者：Tempelmayr, Markus
作者单位：University of Munster
摘要：We give a novel characterization of the centered model in regularity structures which persists for rough drivers even as a mollification fades away. We present our result for a class of quasilinear equations driven by noise, however we believe that the method is robust and applies to a much broader class of subcritical equations. Furthermore, we prove that a convergent sequence of noise ensembles, satisfying uniformly a spectral gap assumption, implies the corresponding convergence of the asso...
