-
作者：Li, Songzi; Li, Xiang-Dong
作者单位：Renmin University of China; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
摘要：We prove the Perelman type W-entropy formula for the geodesic flow on the L-2-Wasserstein space over a complete Riemannian manifold equipped with Otto's infinite dimensional Riemannian metric. To better understand the similarity between the W-entropy formula for the geodesic flow on the Wasserstein space and the W-entropy formula for the heat flow of the Witten Laplacian on the underlying manifold, we introduce the Langevin deformation of flows on the Wasserstein space over a Riemannian manifo...
-
作者：Conforti, Giovanni
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We investigate the quadratic Schrodinger bridge problem, a.k.a. Entropic Optimal Transport problem, and obtain weak semiconvexity and semiconcavity bounds on Schrodinger potentials under mild assumptions on the marginals that are substantially weaker than log-concavity. We deduce from these estimates that Schrodinger bridges satisfy a logarithmic Sobolev inequality on the product space. Our proof strategy is based on a second order analysis of coupling by reflection on the characteristics of t...
-
作者：Dembin, Barbara; Garban, Christophe
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Institut Universitaire de France
摘要：We consider the standard first passage percolation model on Z(d) with a distribution G taking two values 0 < a < b. We study the maximal flow through the cylinder [0, n](d-1) x [0, hn] between its top and bottom as well as its associated minimal surface(s). We prove that the variance of the maximal flow is superconcentrated, i.e. in O( n(d-1) /log n), for h >= h(0) (for a large enough constant h(0) = h(0)(a, b)). Equivalently, we obtain that the ground state energy of a disordered Ising ferrom...
-
作者：Adhikari, Arka; Brennecke, Christian; Xu, Changji; Yau, Horng-Tzer
作者单位：Stanford University; University of Bonn; Harvard University; Harvard University
摘要：We consider general mixed p-spin mean field spin glass models and provide a method to prove that the spectral gap of the Dirichlet form associated with the Gibbs measure is of order one at sufficiently high temperature. Our proof is based on an iteration scheme relating the spectral gap of the N-spin system to that of suitably conditioned subsystems.
-
作者：Barbu, Viorel; Roeckner, Michael
作者单位：Romanian Academy; Alexandru Ioan Cuza University; University of Bielefeld
摘要：This work is concerned with the existence of mild solutions to nonlinear Fokker-Planck equations with fractional Laplace operator ( - Delta ) s \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(- \Delta )<^>s$$\end{document} for s is an element of 1 2 , 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackag...
-
作者：Hofmanova, Martina; Lange, Theresa; Pappalettera, Umberto
作者单位：University of Bielefeld
摘要：We construct Holder continuous, global-in-time probabilistically strong solutions to 3D Euler equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be prescribed a priori up to a stopping time, that can be chosen arbitrarily large with high probability. We also prove that there exist infinitely many Holder continuous initial conditions leading to non-uniqueness of solutions to the Cauchy problem associated with the system. Our construction relies on a flow tr...
-
作者：Lelli, Andrea; Stauffer, Alexandre
作者单位：University of Bath; University of London; King's College London
摘要：We study the mixing time of a random walker who moves inside a dynamical random cluster model on the d-dimensional torus of side-length n. In this model, edges switch at rate mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} between open and closed, following a Glauber dynamics for the random c...
-
作者：Mu, Yingxin; Sapozhnikov, Artem
作者单位：Leipzig University
摘要：We consider connectivity properties of the vacant set of (random) ensembles of Wiener sausages in Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}<^>d$$\end{document} in the transient dimensions d >= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepa...
-
作者：Goldman, Michael; Trevisan, Dario
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; University of Pisa
摘要：We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>d$$\end{document} where the edge cost between two points is given by a pth power of their Euclidean distance. This includes...
-
作者：Gass, Louis; Stecconi, Michele
作者单位：University of Luxembourg
摘要：Let f be a Gaussian random field on Rd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>d$$\end{document} and let X be the number of critical points of f contained in a compact subset. A long-standing conjecture is that, under mild regularity and non-degeneracy conditions on f, the random variable X has...
