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作者：Das, Sayan; Zhu, Weitao
作者单位：Columbia University
摘要：We consider the continuum directed random polymer (CDRP) model that arises as a scaling limit from 1+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+1$$\end{document} dimensional directed polymers in the intermediate disorder regime. We show that for a point-to-point polymer of length t and any p is an element o...
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作者：Blanca, Antonio; Gheissari, Reza
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Northwestern University
摘要：Sampling from the q-state ferromagnetic Potts model is a fundamental question in statistical physics, probability theory, and theoretical computer science. On general graphs, this problem may be computationally hard, and this hardness holds at arbitrarily low temperatures. At the same time, in recent years, there has been significant progress showing the existence of low-temperature sampling algorithms in various specific families of graphs. Our aim in this paper is to understand the minimal s...
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作者：Le Gall, Jean-Francois; Riera, Armand
作者单位：Universite Paris Saclay; Sorbonne Universite; Universite Paris Cite
摘要：We establish a new spatial Markov property of the Brownian half-plane. According to this property, if one removes a hull centered at a boundary point, the remaining space equipped with an intrinsic metric is still a Brownian half-plane, which is independent of the part that has been removed. This is an analog of the well-known peeling procedure for random planar maps. We also investigate several distributional properties of hulls centered at a boundary point, and we provide a new construction ...
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作者：Ang, Morris; Holden, Nina; Sun, Xin; Yu, Pu
作者单位：University of California System; University of California San Diego; New York University; Peking University
摘要：Two-pointed quantum disks with a weight parameter W > 0 is a canonical family of finite-volume random surfaces in Liouville quantum gravity. We prove that the conformal welding of the forested variant of this disk gives a two-pointed quantum disk with an independent SLE kappa for kappa is an element of (4, 8). Furthermore, we show that the conformal welding of multiple forested quantum disks gives a surface arising in Liouville conformal field theory decorated by multiple SLE kappa for kappa i...
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作者：Monmarche, Pierre; Reygner, Julien
作者单位：Sorbonne Universite; Institut Universitaire de France; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：Non-linear versions of log-Sobolev inequalities, that link a free energy to its dissipation along the corresponding Wasserstein gradient flow (i.e. corresponds to Polyak-Lojasiewicz inequalities in this context), are known to provide global exponential long-time convergence to the free energy minimizers, and have been shown to hold in various contexts. However they cannot hold when the free energy admits critical points which are not global minimizers, which is for instance the case of the gra...
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作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We consider the area of spheres centered at the distinguished point in the Brownian plane. As a function of the radius, the resulting process has continuously differentiable sample paths. Furthermore, the pair consisting of the process and its derivative is time-homogeneous Markov and satisfies an explicit stochastic differential equation.
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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：Riabov, Volodymyr
作者单位：Institute of Science & Technology - Austria
摘要：We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear eigenvalue statistics at the cusp-like singularities were not studied in any ensemble. Our analysis covers not only the exact cusps but the entire transitionary regime from the square-root singularity at a regular edge through the sharp cusp to the bulk. We ide...
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作者：Aistleitner, Christoph; Fruehwirth, Lorenz; Prochno, Joscha
作者单位：Graz University of Technology; Graz University of Technology; University of Passau
摘要：It is a classical observation that lacunary function systems exhibit many properties which are typical for systems of independent random variables. However, it had already been observed by Erdos and Fortet in the 1950s that probability theory's limit theorems may fail for lacunary sums n-ary sumation f ( n k x ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setle...
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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 ...
