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作者：Dimitrov, Evgeni; Yang, Zongrui
作者单位：University of Southern California; Columbia University
摘要：We construct a one-parameter family of infinite line ensembles on [0,infinity)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[0, \infty )$$\end{document} that are natural half-space analogues of the Airy line ensemble. Away from the origin these ensembles are locally described by avoiding Brownian bridges, and nea...
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作者：Radhakrishnan, Ritvik Ramanan; Tassion, Vincent
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We discuss a general method to obtain quantitative improvements of correlation inequalities and apply it to arm estimates for Bernoulli bond percolation on Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {Z}}<^>2$$\end{document}. Our first result is that the two-arm exponent is strictly larger than twice...
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作者：Jorritsma, Joost; Komjathy, Julia; Mitsche, Dieter
作者单位：University of Oxford; Delft University of Technology; Pontificia Universidad Catolica de Chile
摘要：We study cluster sizes in supercritical d-dimensional inhomogeneous percolation models with long-range edges -such as long-range percolation- and/or heavy-tailed degree distributions -such as geometric inhomogeneous random graphs and the age-dependent random connection model. Our focus is on large deviations of the size of the largest cluster in the graph restricted to a finite box as its volume tends to infinity. Compared to nearest neighbor Bernoulli bond percolation on Zd\documentclass[12pt...
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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...
