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作者：Jarai, Antal A.; Ruszel, Wioletta M.; Saada, Ellen
作者单位：University of Bath; Delft University of Technology; Utrecht University; Universite Paris Cite; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We show that in Abelian sandpiles on infinite Galton-Watson trees, the probability that the total avalanche has more than t topplings decays as t(-1/2). We prove both quenched and annealed bounds, under suitable moment conditions. Our proofs are based on an analysis of the conductance martingale of Morris (Probab Theory Relat Fields 125:259-265, 2003), thatwas previously used by Lyons et al. (Electron J Probab 13(58):1702-1725, 2008) to study uniform spanning forests on Z(d), d >= 3, and other...
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作者：Brennan, Matthew; Bresler, Guy; Nagaraj, Dheeraj
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Random graphs with latent geometric structure are popular models of social and biological networks, with applications ranging from network user profiling to circuit design. These graphs are also of purely theoretical interest within computer science, probability and statistics. A fundamental initial question regarding these models is: when are these random graphs affected by their latent geometry and when are they indistinguishable from simpler models without latent structure, such as the Erdo...
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作者：Roeckner, Michael; Xie, Longjie; Zhang, Xicheng
作者单位：University of Bielefeld; Jiangsu Normal University; Wuhan University
摘要：We prove the superposition principle for probability measure-valued solutions to non-local Fokker-Planck-Kolmogorov equations, which in turn yields the equivalence between martingale problems for stochastic differential equations with jumps and such non-local partial differential equations with rough coefficients. As an application, we obtain a probabilistic representation for weak solutions of fractional porous media equations.
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作者：FitzGerald, Will; Warren, Jon
作者单位：University of Sussex; University of Warwick
摘要：This paper proves an equality in law between the invariant measure of a reflected system of Brownian motions and a vector of point-to-line last passage percolation times in a discrete random environment. A consequence describes the distribution of the all-time supremum of Dyson Brownian motion with drift. A finite temperature version relates the point-to-line partition functions of two directed polymers, with an inverse-gamma and a Brownian environment, and generalises Dufresne's identity. Our...
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作者：Ganguly, Shirshendu; Sarkar, Sourav
作者单位：University of California System; University of California Berkeley; University of Toronto
摘要：Stochastic point processes with Coulomb interactions arise in various natural examples of statistical mechanics, random matrices and optimization problems. Often such systems due to their natural repulsion exhibit remarkable hyperuniformity properties, that is, the number of points landing in any given region fluctuates at a much smaller scale compared to that of a set of i.i.d. random points. A well known conjecture from physics appearing in the works of Jancovici, Lebowitz, Manificat, Martin...
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作者：Bourgade, P.; Dubach, G.
作者单位：New York University
摘要：We study the overlaps between eigenvectors of nonnormal matrices. They quantify the stability of the spectrum, and characterize the joint eigenvalues increments under Dyson-type dynamics. Well known work by Chalker and Mehlig calculated the expectation of these overlaps for complex Ginibre matrices. For the same model, we extend their results by deriving the distribution of diagonal overlaps (the condition numbers), and their correlations. We prove: (i) convergence of condition numbers for bul...
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作者：Menz, Georg; Tassy, Martin
作者单位：University of California System; University of California Los Angeles; Dartmouth College
摘要：We show the existence of a variational principle for graph homomorphisms from Z(m) to a d-regular tree. The technique is based on a discrete Kirszbraun theorem and a concentration inequality obtained through the dynamics of the model. As another consequence of the concentration inequality we also obtain the existence of a continuum of translation-invariant ergodic gradient Gibbs measures for graph homomorphisms from Z(m) to a regular tree. The method is sufficiently robust such that it could b...
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作者：Beliaev, Dmitry; McAuley, Michael; Muirhead, Stephen
作者单位：University of Oxford; University of London; King's College London; University of London; Queen Mary University London
摘要：The Nazarov-Sodin constant describes the average number of nodal set components of smooth Gaussian fields on large scales. We generalise this to a functional describing the corresponding number of level set components for arbitrary levels. Using results from Morse theory, we express this functional as an integral over the level densities of different types of critical points, and as a result deduce the absolute continuity of the functional as the level varies. We further give upper and lower b...
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作者：He, Yukun; Knowles, Antti
作者单位：University of Zurich; University of Geneva
摘要：We investigate to what extent the microscopic Wigner-Gaudin-Mehta-Dyson (WGMD) (or sine kernel) statistics of random matrix theory remain valid on mesoscopic scales. To that end, we compute the connected two-point spectral correlation function of a Wigner matrix at two mesoscopically separated points. In the mesoscopic regime, density correlations are much weaker than in the microscopic regime. Our result is an explicit formula for the two-point function. This formula implies that the WGMD sta...
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作者：Lupu, Titus; Sabot, Christophe; Tarres, Pierre
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; New York University; NYU Shanghai; Universite PSL; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
摘要：We introduce a continuous space limit of the vertex reinforced jump process (VRJP) in dimension one, which we call linearly reinforced motion (LRM) on R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}$$\end{document}. It is constructed out of a convergent Bass-Burdzy flow. The proof goes through the repr...
