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作者：Ahidar-Coutrix, A.; Le Gouic, T.; Paris, Q.
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); HSE University (National Research University Higher School of Economics)
摘要：This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumption is termed a variance inequality and provides a strong connection between usual assumptions in the field of empirical processes and central concepts of metric geometry. We study the validity of variance inequalities in spaces of non-positive and non-negative Aleksandrov curvature. In this last scenar...
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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：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：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：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...
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作者：Ding, Jian; Fukushima, Ryoki; Sun, Rongfeng; Xu, Changji
作者单位：University of Pennsylvania; Kyoto University; National University of Singapore; University of Chicago
摘要：We consider a discrete time simple symmetric random walk among Bernoulli obstacles on Z(d), d >= 2, where the walk is killed when it hits an obstacle. It is known that conditioned on survival up to time N, the random walk range is asymptotically contained in a ball of radius (sic)N = CN1/(d+ 2) for any d = 2. For d = 2, it is also known that the range asymptotically contains a ball of radius (1-) N for any > 0, while the case d = 3 remains open. We complete the picture by showing that for any ...
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作者：Dumaz, Laure; Labbe, Cyril
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS)
摘要：We study the bottom of the spectrum of the Anderson Hamiltonian H-L := -partial derivative(2)(x) + xi on [0, L] driven by a white noise xi and endowed with either Dirichlet or Neumann boundary conditions. We show that, as L -> infinity, the point process of the (appropriately shifted and rescaled) eigenvalues converges to a Poisson point process on R with intensity e(x)dx, and that the (appropriately rescaled) eigenfunctions converge to Dirac masses located at independent and uniformly distrib...
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作者：Gassiat, Paul; Gess, Benjamin; Lions, Pierre-Louis; Souganidis, Panagiotis E.
作者单位：Universite PSL; Universite Paris-Dauphine; Max Planck Society; University of Bielefeld; Universite PSL; College de France; University of Chicago
摘要：We show that the initial value problem for Hamilton-Jacobi equations with multiplicative rough time dependence, typically stochastic, and convex Hamiltonians satisfies finite speed of propagation. We prove that in general the range of dependence is bounded by a multiple of the length of the skeleton of the path, that is a piecewise linear path obtained by connecting the successive extrema of the original one. When the driving path is a Brownian motion, we prove that its skeleton has almost sur...
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作者：Lambert, Amaury; Schertzer, Emmanuel
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Biology (INSB); Universite PSL; College de France; Ecole Normale Superieure (ENS); Institut National de la Sante et de la Recherche Medicale (Inserm)
摘要：The nested Kingman coalescent describes the dynamics of particles (called genes) contained in larger components (called species), where pairs of species coalesce at constant rate and pairs of genes coalesce at constant rate provided they lie within the same species. We prove that starting from rn species, the empirical distribution of species masses (numbers of genes/n) at time t/n converges as n -> infinity to a solution of the deterministic coagulation-transport equation partial derivative(t...
