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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.
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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...
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作者：Baraud, Yannick
作者单位：University of Luxembourg
摘要：In the Bayes paradigm, given a loss function and an n-sample, we present the construction of a new type of posterior distribution, that extends the classical Bayes one. The loss functions we have in mind are either those derived from the total variation and Hellinger distances or some L-j-ones for j > 1. We prove that, with a probability close to one, this new posterior distribution concentrates its mass in a neighbourhood (for the chosen loss function) of the law of the data, provided that th...
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作者：Liu, Yucheng; Slade, Gordon
作者单位：University of British Columbia
摘要：We give conditions on a real-valued function F on Z(d), for d>2, which ensure that the solution G to the convolution equation (F & lowast;G)(x)=delta(0,x) has Gaussian decay |x|(-(d-2)) for large |x|. Precursors of our results were obtained in the 2000s, using intricate Fourier analysis. In 2022, a very simple deconvolution theorem was proved, but its applicability was limited. We extend the 2022 theorem to remove its limitations while maintaining its simplicity -- our main tools are H & ouml;...
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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...
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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...
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作者：Brazitikos, Silouanos; Giannopoulos, Apostolos; Pafis, Minas
作者单位：National & Kapodistrian University of Athens
摘要：Given a probability measure mu on R-n, Tukey's half-space depth is defined for any x is an element of R-n by phi(mu)(x) = inf{mu (H) : H is an element of H(x)}, where H(x) is the set of all half-spaces H of R-n containing x. We show that if mu is a non-degenerate log-concave probability measure on R-n thene(-c1n) <= integral (n)(R)phi mu (x) d mu (x) <= e(mu)(-c2n/L2)where L-mu is the isotropic constant of mu and c(1), c(2) > 0 are absolute constants. The proofs combine large deviations techni...
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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...
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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...
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作者：Mikulincer, Dan; Shenfeld, Yair
作者单位：Massachusetts Institute of Technology (MIT); Brown University
摘要：Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual construction of such maps, however, is a non-trivial task and, so far, relies mostly on the theory of optimal transport. In this work, we take advantage of the infinite-dimensional nature of the Gaussian measure and construct a new transport map, based on the F & ouml;llmer process, which pushes forward the Wiener measure onto probability measures on...
