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作者：Clozeau, Nicolas; Mattesini, Francesco
作者单位：Institute of Science & Technology - Austria; University of Munster; Max Planck Society
摘要：We study a random matching problem on closed compact 2-dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers n and m = m(n) of points, asymptotically equivalent as n goes to infinity, the optimal transport plan between the two empirical measures mu(n) and v(m) is quantitat...
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作者：Berestycki, Nathanael; van Engelenburg, Diederik
作者单位：University of Vienna
摘要：We prove that for recurrent, reversible graphs, the following conditions are equivalent: (a) existence and uniqueness of the potential kernel, (b) existence and uniqueness of harmonic measure from infinity, (c) a new anchored Harnack inequality, and (d) one-endedness of the wired uniform spanning tree. In particular this gives a proof of the anchored (and in fact also elliptic) Harnack inequality on the UIPT. This also complements and strengthens some results of Benjamini et al. (Ann Probab 29...
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作者：Yan, Shuo
作者单位：University System of Maryland; University of Maryland College Park
摘要：We consider coupled slow-fast stochastic processes, where the averaged slow motion is given by a two-dimensional Hamiltonian system with multiple critical points. On a proper time scale, the evolution of the first integral converges to a diffusion process on the corresponding Reeb graph, with certain gluing conditions specified at the interior vertices, as in the case of additive white noise perturbations of Hamiltonian systems considered by M. Freidlin and A. Wentzell. The current paper provi...
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作者：Moench, Christian
作者单位：Johannes Gutenberg University of Mainz
摘要：We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent random connection model and several other previously investigated models. Our focus is on the weak decay regime, in which inter-cluster long-range connection probabilities fall off polynomially with small exponent, and for which we establish several structural properties. Chief among them are the continuity of the bond percolation function and the tra...
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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...
