作者：Asselah, Amine; Schapira, Bruno; Sousi, Perla
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge
摘要：We consider branching random walks on the Euclidean lattice mostly in dimensions five and higher. In this non-Markovian setting, we derive upper bounds for the probability of spending a fixed time in each ball of an arbitrary finite collection of balls. These bounds involve the branching capacity introduced by Zhu (On the critical branching random walk I: branching capacity and visiting probability, arXiv:1611.10324). For random walks, the analogous tail estimates have been instrumental in tac...
作者：Ding, Jian; Sun, Nike
作者单位：Peking University; Massachusetts Institute of Technology (MIT)
摘要：We consider the Ising perceptron with gaussian disorder, which is equivalent to the discrete cube {-1,+1}N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{-1,+1\}<^>N$$\end{document} intersected by M random half-spaces. The perceptron's capacity is the largest integer MN\documentclass[12pt]{minimal} \usepackage{am...
