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作者：Bedrossian, Jacob; Liss, Kyle
作者单位：University of California System; University of California Los Angeles; Duke University
摘要：A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In this work we explore this in (finite-dimensional) stochastic differential equations in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\...
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作者：Horst, Ulrich; Xu, Wei
作者单位：Humboldt University of Berlin; Humboldt University of Berlin; Beijing Institute of Technology
摘要：We prove that the long-run behavior of Hawkes processes is fully determined by the average number and the dispersion of child events. For subcritical processes we provide FLLNs and FCLTs under minimal conditions on the kernel of the process with the precise form of the limit theorems depending strongly on the dispersion of child events. For a critical Hawkes process with weakly dispersed child events, functional central limit theorems do not hold. Instead, we prove that the rescaled intensity ...
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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. ...
