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作者：Husson, Jonathan; Ko, Justin
作者单位：University of Michigan System; University of Michigan; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We consider the asymptotics of rank k spherical integrals when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k = o(N)$$\end{document}. We prove that the sublinear rank spherical integrals are approximately the products of rank 1 spherical integrals. Our formulas extend the results for rank k spherical integrals p...
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作者：Cannizzaro, G.; Goncalves, P.; Misturini, R.; Occelli, A.
作者单位：University of Warwick; Universidade de Lisboa; Universidade Federal do Rio Grande do Sul; Universite d'Angers
摘要：We study the equilibrium fluctuations of an interacting particle system evolving on the discrete ring with N is an element of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\in {\mathbb {N}}$$\end{document} points, denoted by TN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{a...
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作者：Maltsev, Anna; Osman, Mohammed
作者单位：University of London; Queen Mary University London
摘要：We consider NxN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\times N$$\end{document} matrices with complex entries that are perturbed by a complex Gaussian matrix with small variance. We prove that if the unperturbed matrix satisfies certain local laws then the bulk correlation functions are universal in the la...
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作者：Garcia, Ernesto; Lessa, Pablo
作者单位：Universidad de la Republica, Uruguay
摘要：We prove that the harmonic measures of certain finite range random walks on Fuchsian Schottky groups, have dimension strictly smaller than the Hausdorff dimension of the corresponding limit set.
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作者：Su, Yiming; Zhang, Deng
作者单位：Hangzhou Normal University; Shanghai Jiao Tong University
摘要：We study the bubbling phenomena for focusing mass-critical nonlinear Schr & ouml;dinger equations, driven by linear multiplicative noise in the sense of controlled rough paths. In both dimensions one and two, we give a pathwise construction of stochastic multi-bubble blow-up solutions, which concentrate at finitely many distinct points, and behave asymptotically like a sum of pseudo-conformal blow-up solutions. In particular, this provides the first examples of mass quantization phenomenon in ...
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作者：Fredes, Luis; Sepulveda, Avelio
作者单位：Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile
摘要：The (non-spanning) tree decorated quadrangulation is a random pair consisting of a quadrangulation and a subtree chosen uniformly over the set of pairs with a prescribed size. In this paper, we study the tree decorated quadrangulation in the critical regime: when the number f of faces of the map is proportional to the square of the size of the tree. We show that with high probability in this regime, the diameter of the tree lies between o(f(1/4)) and f(1/4)/log(alpha)(f), for all alpha > 1. Th...
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作者：Huang, Han; Tikhomirov, Konstantin
作者单位：University of Missouri System; University of Missouri Columbia; Carnegie Mellon University
摘要：Given a positive integer n, an unlabeled graph G on n vertices, and a vertex v of G, let N-G(v) be the subgraph of G induced by vertices of G of distance at most one from v. We show that there are universal constants C, c > 0 with the following property. Let the sequence (p(n))(n=1)(8) satisfy n(-1/2) log(n)(C) <= pn <= c. For each n, let Gamma(n) be an unlabeled G(n, p(n)) Erdos-Renyi graph. Then with probability 1 - o(n)(1), any unlabeled graph (Gamma) over tilde (n) on n vertices with {N (G...
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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：Parraud, Felix; Schnelli, Kevin
作者单位：Royal Institute of Technology
摘要：In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of polynomials evaluated in those matrices. We prove an asymptotic expansion in the inverse of the matrix dimension to any order. Out of this result we deduce new formulas for map enumerations and the microstates free entropy. Our approach is based on the interpolatio...
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作者：Delarue, Francois; Hammersley, William R. P.
作者单位：Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：The purpose of this work is to provide an explicit construction of a strong Feller semigroup on the space of probability measures over the real line that additionally maps bounded measurable functions into Lipschitz continuous functions, with a Lipschitz constant that blows up in an integrable manner in small time. Our construction relies on a rearranged version of the stochastic heat equation on the circle driven by a coloured noise. Formally, this stochastic equation writes as a reflected eq...
