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作者：Hutchcroft, Tom
作者单位：University of Cambridge
摘要：Let G be a Cayley graph of a nonamenable group with spectral radius rho<1. It is known that branching random walk on G with offspring distribution mu is transient, i.e., visits the origin at most finitely often almost surely, if and only if the expected number of offspring mu over bar satisfies mu over bar <=rho-1. Benjamini and Muller (Groups Geom Dyn, 6:231-247, 2012) conjectured that throughout the transient supercritical phase 1
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作者：Chiarini, Alberto; Nitzschner, Maximilian
作者单位：University of California System; University of California Los Angeles; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We investigate level-set percolation of the discrete Gaussian free field on Zd, d = 3, in the strongly percolative regime. We consider the event that the level-set of theGaussian free field below a level a disconnects the discrete blow-up of a compact set A. Rd from the boundary of an enclosing box. We derive asymptotic large deviation upper bounds on the probability that the local averages of theGaussian free field deviate from a specific multiple of the harmonic potential of A, when disconne...
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作者：Dubedat, Julien; Falconet, Hugo; Gwynne, Ewain; Pfeffer, Joshua; Sun, Xin
作者单位：Columbia University; University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：For gamma is an element of (0, 2), we define a weak gamma-Liouville quantum gravity (LQG) metric to be a function h -> D-h which takes in an instance of the planar Gaussian free field and outputs a metric on the plane satisfying a certain list of natural axioms. We showthat these axioms are satisfied for any subsequential limits of Liouville first passage percolation. Such subsequential limits were proven to exist by Ding et al. (Tightness of Liouville first passage percolation for gamma is an...
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作者：Prigent, Martin; Roberts, Matthew I.
作者单位：University of Bath
摘要：We define a dynamical simple symmetric random walk in one dimension, and show that there almost surely exist exceptional times at which the walk tends to infinity. This is in contrast to the usual dynamical simple symmetric random walk in one dimension, for which such exceptional times are known not to exist. In fact we show that the set of exceptional times has Hausdorff dimension 1/2 almost surely, and give bounds on the rate at which the walk diverges at such times. We also show noise sensi...
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作者：Merkl, Franz; Rolles, Silke W. W.; Tarres, Pierre
作者单位：University of Munich; Technical University of Munich; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Universite PSL; Universite Paris-Dauphine
摘要：In the original publication, Acknowledgements section was incorrect. The correct Acknowledgements is given below.
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作者：Barchiesi, Marco; Julin, Vesa
作者单位：University of Naples Federico II; University of Jyvaskyla
摘要：We study an isoperimetric problem described by a functional that consists of the standard Gaussian perimeter and the norm of the barycenter. The second term is in competition with the perimeter, balancing the mass with respect to the origin, and because of that the solution is not always the half-space. We characterize all the minimizers of this functional, when the volume is close to one, by proving that the minimizer is either the half-space or the symmetric strip, depending on the strength ...
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作者：Lytova, Anna; Tikhomirov, Konstantin
作者单位：University of Opole; University System of Georgia; Georgia Institute of Technology
摘要：We study delocalization of null vectors and eigenvectors of random matrices with i.i.d entries. Let A be an 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}|I|=m||vI||>= m3/2n3/2logCn||v||\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepa...
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作者：Eldan, Ronen
作者单位：Weizmann Institute of Science
摘要：The analysis of various models in statistical physics relies on the existence of decompositions of measures into mixtures of product-like components, where the goal is to attain a decomposition into measures whose entropy is close to that of the original measure, yet with small correlations between coordinates. We prove a related general result: For every measure mu on Rn and every epsilon>0, there exists a decomposition mu=integral mu theta dm(theta) such that H(mu)-E theta similar to mH(mu t...
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作者：Miller, Jason; Qian, Wei
作者单位：University of Cambridge
摘要：We prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necessarily singular with respect to the law of any type of SLE kappa. These hypotheses are satisfied by the LQG metric for gamma = root 8/3 constructed by the first author and Sheffield, and subsequent work by Gwynne and the first author has shown that there is a unique metric which satisfies these hypotheses for each gamma is an element of (0, 2...
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作者：Grama, Ion; Lauvergnat, Ronan; Le Page, Emile
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Let (Xn) n0 be a Markov chain with values in a finite state space X starting at X0 = x. X and let f be a real function defined on X. Set Sn = nk =1 f ( Xk), n 1. For any y. R denote by ty the first time when y + Sn becomes non-positive. We study the asymptotic behaviour of the probability Px y + Sn. [z, z + a], ty > n as n.+8. We first establish for this probability a conditional version of the local limit theorem of Stone. Then we find for it an asymptotic equivalent of order n3/2 and give a ...
