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作者：Narayanan, Hariharan; Sheffield, Scott; Tao, Terence
作者单位：Tata Institute of Fundamental Research (TIFR); Massachusetts Institute of Technology (MIT); University of California System; University of California Los Angeles
摘要：Associated to two given sequences of eigenvalues lambda(1) >= ... >=lambda(n) and mu(1) >= ... = mu(n) is a natural polytope, the polytope of augmented hives with the specified boundary data, which is associated to sums of random Hermitian matrices with these eigenvalues. As a first step towards the asymptotic analysis of random hives, we show that if the eigenvalues are drawn from the GUE ensemble, then the associated augmented hives exhibit concentration as n -> infinity. Our main ingredient...
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作者：Landon, Benjamin; Lopatto, Patrick; Sosoe, Philippe
作者单位：University of Toronto; Brown University; Cornell University
摘要：We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue around its classical location are Gaussian with a universal variance. Our method is based on a dynamical approach to mesoscopic linear spectral statistics which reduces their behavior on short scales to that on larger scales. We prove a central limit theorem fo...
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作者：Bormann, Marie; von Renesse, Max; Wang, Feng-Yu
作者单位：Leipzig University; Max Planck Society; Tianjin University
摘要：We prove geometric upper bounds for the Poincar & eacute; and Logarithmic Sobolev constants for Brownian motion on manifolds with sticky reflecting boundary diffusion i.e. extended Wentzell-type boundary condition under general curvature assumptions on the manifold and its boundary. The method is based on an interpolation involving energy interactions between the boundary and the interior of the manifold. As side results we obtain explicit geometric bounds on the first nontrivial Steklov eigen...
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作者：Das, Sayan; Drillick, Hindy; Parekh, Shalin
作者单位：University of Chicago; Columbia University; University System of Maryland; University of Maryland College Park
摘要：We show that under a certain moderate deviation scaling, the multiplicative-noise stochastic heat equation (SHE) arises as the fluctuations of the quenched density of a 1D random walk whose transition probabilities are iid [0,1]-valued random variables. In contrast to the case of directed polymers in the intermediate disorder regime, the variance of our weights is fixed rather than vanishing under the diffusive rescaling of space-time. Consequently, taking a naive limit of the chaos expansion ...
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作者：Dung, Nguyen Tien
作者单位：Vietnam National University Hanoi (VNU Hanoi) System; Vietnam National University Ho Chi Minh City (VNUHCM) System
摘要：We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive quantitative estimates for the Fisher information distance. To illustrate the applicability of our approach, explicit rates of Fisher information convergence for quadratic forms and the functions of sample means are provided. For the sums of independent random...
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作者：Bresar, Miha; Mijatovic, Aleksandar
作者单位：University of Warwick
摘要：We provide a criterion for establishing lower bounds on the rate of convergence in f-variation of a continuous-time ergodic Markov process to its invariant measure. The criterion consists of novel super- and submartingale conditions for certain functionals of the Markov process. It provides a general approach for proving lower bounds on the tails of the invariant measure and the rate of convergence in f-variation of a Markov process, analogous to the widely used Lyapunov drift conditions for u...
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作者：Eberle, Andreas; Loerler, Francis
作者单位：University of Bonn
摘要：We propose a new concept of lifts of reversible diffusion processes and show that various well-known non-reversible Markov processes arising in applications are lifts in this sense of simple reversible diffusions. Furthermore, we introduce a concept of non-asymptotic relaxation times and show that these can at most be reduced by a square root through lifting, generalising a related result in discrete time. Finally, we demonstrate how the recently developed approach to quantitative hypocoercivi...
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作者：Bovier, Anton; Schertzer, Adrien
作者单位：University of Bonn
摘要：20 years ago, Bovier, Kurkova, and L & ouml;we (Ann Probab 30(2):605-651, 2002) proved a central limit theorem (CLT) for the fluctuations of the free energy in the p-spin version of the Sherrington-Kirkpatrick model of spin glasses at high temperatures. In this paper we improve their results in two ways. First, we extend the range of temperatures to cover the entire regime where the quenched and annealed free energies are known to coincide. Second, we identify the main source of the fluctuatio...
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作者：Feng, Yu; Peltola, Eveliina; Wu, Hao
作者单位：Tsinghua University; Aalto University; University of Bonn
摘要：We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight q is an element of [ 1 , 4 ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsf...
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作者：Dolera, Emanuele; Favaro, Stefano; Mainini, Edoardo
作者单位：University of Pavia; University of Turin; University of Genoa
摘要：In Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In this paper, we develop a new approach to PCRs, with respect to strong norm distances on parameter spaces of functions. Critical to our approach is the combination of a local Lipschitz-continuity for the posterior distribution with a dynamic formulation of the ...
