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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：Universite Paris Cite; 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：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：Ammari, Zied; Rout, Andrew; Sohinger, Vedran
作者单位：Universite Marie et Louis Pasteur; Polytechnic University of Milan; University of Warwick
摘要：In this paper, we are concerned with the study of statistical equilibria for focusing nonlinear Schr & ouml;dinger and Hartree equations on the d-dimensional torus Td\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {T}<^>d$$\end{document} when d=1,2,3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepac...
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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：Enriquez, Nathanael; Liu, Mike; Menard, Laurent; Perchet, Vianney
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider sequences of finite weighted random graphs that converge locally to unimodular i.i.d. weighted random trees. When the weights are atomless, we prove that the matchings of maximal weight converge locally to a matching on the limiting tree. For this purpose, we introduce and study unimodular matchings on weighted unimodular random trees as well as a notion of optimality for these objects. In this context, we prove that, in law, there is a unique optimal unimodular matching for a give...
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作者：He, Yukun
作者单位：Fudan University
摘要：Let A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}$$\end{document} be the adjacency matrix of the Erd & odblac;s-R & eacute;nyi directed graph G(N,p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mat...
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作者：Adhikari, Arka; Park, Jiyun
作者单位：University System of Maryland; University of Maryland College Park; Stanford University
摘要：We prove a moderate deviation principle for the capacity of the range of random walk in Z5 . Depending on the scale of deviation, we get two different regimes. We observe Gaussian tails when the deviation scale is smaller than n1/2(logn)3/4 . Otherwise, we get non-Gaussian tails with a constant arising from a generalized Gagliardo-Nirenberg inequality. This is analogous to the behavior of the volume of the random walk range in Z3 . Our methods can also be applied to the d=4 case to prove the m...
