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作者：Gu, Yu; Komorowski, Tomasz
作者单位：University System of Maryland; University of Maryland College Park; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：For the KPZ equation on a torus with a 1+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+1$$\end{document} spacetime white noise, it was shown in Dunlap et al. (Commun Pure Appl Math, 2023, https://doi.org/10.1002/cpa.22110) and Gu and Komorowski (Ann Inst H Poincare Prob Stat, 2021, arXiv:2104.13540v2) that the...
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作者：Montanari, Andrea; Zhong, Yiqiao; Zhou, Kangjie
作者单位：Stanford University; Stanford University; University of Wisconsin System; University of Wisconsin Madison
摘要：In the negative perceptron problem we are given n data points (xi,yi)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\varvec{x}_i,y_i)$$\end{document}, where xi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs...
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作者：Collin, Orphee; Giacomin, Giambattista; Hu, Yueyun
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris 13
摘要：We consider the continuum version of the random field Ising model in one dimension: this model arises naturally as weak disorder scaling limit of the original Ising model. Like for the Ising model, a spin configuration is conveniently described as a sequence of spin domains with alternating signs (domain-wall structure). We show that for fixed centered external field and as spin-spin couplings become large, the domain-wall structure scales to a disorder dependent limit that coincides with the ...
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作者：Sah, Ashwin; Sawhney, Mehtaab
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Answering a pair of questions of Conrey, Gabbard, Grant, Liu, and Morrison, we prove that a triplet of dice drawn from the multiset modelare intransitive with probability 1/4+o(1)and the probability a random pair of dice tie tends toward alpha n(-1) for an explicitly defined constant alpha. This extends and sharpens the recent results of Polymath regarding the balanced sequence model. We further show the distribution of larger tournaments converges to a universal tournamenton in both models. T...
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作者：Bhamidi, Shankar; Sen, Sanchayan
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Indian Institute of Science (IISC) - Bangalore
摘要：A well-known open problem on the behavior of optimal paths in random graphs in the strong disorder regime, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade (Braunstein et al. in Phys RevLett 91(16):168701, 2003; Braunstein et al. in Int J Bifurc Chaos 17(07):2215-2255,2007; Chen et al. in Phys Rev Lett 96(6):068702, 2006; Wu et al. in Phys Rev Lett96(14):148702, 2006) is as follows: for a large class of random graph models with de...
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作者：Carlier, Guillaume; Delalande, Alex; Merigot, Quentin
作者单位：Universite PSL; Universite Paris-Dauphine; Inria; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Institut Universitaire de France
摘要：Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or language processing. In these fields however, the probability measures of interest are often not accessible in their entirety and the practitioner may have to deal with statistical or computational approximations instead. In this article, we quantify the effect of such approximations on the corresponding barycenters. ...
