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作者：Hilario, Marcelo; Sa, Marcos; Sanchis, Remy; Teixeira, Augusto
作者单位：Universidade Federal de Minas Gerais; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universidade de Lisboa
摘要：In this article, we consider a variety of percolation models on randomly stretched lattices. The first model we study is constructed on the usual square grid Z(2), keeping all vertices untouched while erasing edges according to the following procedure: for every integer i, the entire column of vertical edges contained in the line {x = i} is removed independently of other columns with probability rho > 0. Similarly, for every integer j, the entire row of horizontal edges contained in the line {...
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作者：Le Gall, Jean-Francois; Riera, Armand
作者单位：Universite Paris Cite; Sorbonne Universite
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：Dubach, Victor
作者单位：Uppsala University
摘要：We propose a new approach to conjugation-invariant random permutations. Namely, we explain how to construct uniform permutations in given conjugacy classes from certain point processes in the plane. This enables the use of geometric tools to study various statistics of such permutations. For their longest decreasing subsequences, we prove universality of the 2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} ...
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作者：Avena, Luca; van der Hofstad, Remco; den Hollander, Frank; Nagy, Oliver
作者单位：University of Florence; Eindhoven University of Technology; Leiden University; Leiden University - Excl LUMC
摘要：We analyse the mixing profile of a random walk on a dynamic random permutation, focusing on the regime where the walk evolves much faster than the permutation. Two types of dynamics generated by random transpositions are considered: one allows for coagulation of permutation cycles only, the other allows for both coagulation and fragmentation. We show that for both types, after scaling time by the length of the permutation and letting this length tend to infinity, the total variation distance b...
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作者：Angel, Omer; Senizergues, Delphin
作者单位：University of British Columbia; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper we prove a scaling limit result for the component of the root in the Wired Minimal Spanning Forest (WMSF) of the Poisson-Weighted Infinite Tree (PWIT), where the latter tree arises as the local weak limit of the Minimal Spanning Tree (MST) on the complete graph endowed with i.i.d. weights on its edges. The limiting object M infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mat...
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作者：Van Den Berg, Jacob; Nolin, Pierre
作者单位：Centrum Wiskunde & Informatica (CWI); City University of Hong Kong
摘要：In the classical Drossel-Schwabl forest fire process, vertices of a lattice become occupied at rate 1, and they are hit by lightning at some tiny rate zeta > 0, which causes entire connected components to burn. In this paper, we study a variant where fires are coming from the boundary of the forest instead. In particular we prove for every positive zeta (including zeta = infinity) that, for the forest fire process without recoveries on an N x N box in the triangular lattice, where each point o...
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作者：Duminil-Copin, Hugo; Panis, Romain
作者单位：Universite Paris Saclay; University of Geneva
摘要：This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions d > 4. Among other results, we obtain up-to-constant estimates for the full-space and half-space two-point functions in the critical and near-critical regimes. A companion paper proposes a similar analysis for spread-out Bernoulli percolation in dimensions d > 6 [10].
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作者：Choi, Inhyeok
作者单位：Korea Institute for Advanced Study (KIAS)
摘要：Let G be a countable group whose action on a metric space X involves a contracting isometry. This setting naturally encompasses groups acting on Gromov hyperbolic spaces, Teichm & uuml;ller space, Culler-Vogtmann Outer space and CAT(0) spaces. We discuss continuity and differentiability of the escape rate of random walks on G. For relatively hyperbolic groups, CAT(-1) groups and CAT(0) cubical groups, we further discuss analyticity of the escape rate. Finally, assuming that the action of G on ...
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作者：Cannizzaro, Giuseppe; Giles, Harry
作者单位：University of Warwick
摘要：We investigate the large-scale behaviour of the Self-Repelling Brownian Polymer (SRBP) in the critical dimension d=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d=2$$\end{document}. The SRBP is a model of self-repelling motion, which is formally given by the solution to a stochastic differential equation driven ...
