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作者：Champagnat, Nicolas; Strickler, Edouard; Villemonais, Denis
作者单位：Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); Inria; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Institut Universitaire de France
摘要：For general penalized Markov processes with soft killing, we propose a simple criterion ensuring uniform convergence of conditional distributions in Wasserstein distance to a unique quasi-stationary distribution. We give several examples of application where our criterion can be checked, including Bernoulli convolutions and piecewise deterministic Markov processes of the form of switched dynamical systems, for which convergence in total variation is not possible.
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作者：Cai, Zhenhao; Ding, Jian
作者单位：Peking University
摘要：In this paper, we study the critical level-set of Gaussian free field (GFF) on the metric graph Z(d), d > 6. We prove that the one-arm probability (i.e. the probability of the event that the origin is connected to the boundary of the box B(N)) is proportional to N-2, where B(N) is centered at the origin and has side length 2 left perpendicular N right perpendicular. Our proof is highly inspired by Kozma and Nachmias (J Am Math Soc 24(2):375-409, 2011) which proves the analogous result for the ...
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作者：Gheissari, Reza; Lubetzky, Eyal
作者单位：Northwestern University; New York University
摘要：We study Glauber dynamics for the low temperature (2 +1)D Solid-On-Solid model on a box of side-length n with a floor at height 0 (inducing entropic repulsion) and a competing bulk external field lambda pointing down (the prewetting problem). In 1996, Cesi and Martinelli showed that if the inverse-temperature beta is large enough, then along a decreasing sequence of critical points (lambda((k)K beta)(c)(k=0) the dynamics is torpid: its inverse spectral gap is O(1) when lambda is an element of ...
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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; 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...
