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作者：De Vecchi, Francesco; Fresta, Luca; Gordina, Maria; Gubinelli, Massimiliano
作者单位：University of Pavia; Roma Tre University; University of Connecticut; University of Oxford
摘要：We introduce a theory of non-commutative L-p spaces suitable for non-commutative probability in a non-tracial setting and use it to develop stochastic analysis of Grassmann-valued processes, including martingale inequalities, stochastic integrals with respect to Ito-Grassmann processes, Girsanov's formula and a weak formulation of Grassmann SDEs. We apply this new setting to the construction of several unbounded random variables including a Grassmann analog of the Phi(2)(4) Euclidean QFT in a ...
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作者：Asselah, Amine; Schapira, Bruno; Sousi, Perla
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); 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...
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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...
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作者：Asselah, Amine; Okada, Izumi; Schapira, Bruno; Sousi, Perla
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Chiba University; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge
摘要：We show that the range of a critical branching random walk conditioned to survive forever and the Minkowski sum of two independent simple random walk ranges are intersection-equivalent in any dimension d >= 5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\ge 5$$\end{document}, in the sense that they hit any finit...
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作者：Herry, Ronan; Malicet, Dominique; Poly, Guillaume
作者单位：Universite de Rennes; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：We study the regularity of the law of a quadratic form Q(X, X), evaluated in a sequence X = ( Xi) of independent and identically distributed random variables, when X1 can be expressed as a sufficiently smooth function of a Gaussian field. This setting encompasses a large class of important and frequently used distributions, such as, among others, Gaussian, Beta, for instance uniform, Gamma distributions, or else any polynomial transform of them. Let us present an emblematic application. Take X...
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作者：Drewitz, Alexander; Prevost, Alexis; Rodriguez, Pierre-Francois
作者单位：University of Cologne; University of Geneva; Imperial College London
摘要：For a large class of amenable transient weighted graphs G, we prove that the sign clusters of the Gaussian free field on G fall into a regime of strong supercriticality, in which two infinite sign clusters dominate (one for each sign), and finite sign clusters are necessarily tiny, with overwhelming probability. Examples of graphs belonging to this class include regular lattices such as Z d \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackag...
