-
作者：Gorski, Christian
作者单位：Northwestern University
摘要：We prove a strict monotonicity theorem for first passage percolation on any Cayley graph of a virtually nilpotent group which is not isomorphic to the standard Cayley graph of Z: given two distributions v and v with finite mean, if v is strictly more variable than v and v is subcritical in an appropriate sense, then the expected passage times associated to v exceed those of v by an amount proportional to the graph distance. This generalizes a theorem of van den Berg and Kesten from 1993, which...
-
作者：Tikhomirov, Konstantin; Youssef, Pierre
作者单位：University System of Georgia; Georgia Institute of Technology; New York University; New York University Abu Dhabi
摘要：In this work we develop a comparison procedure for the modified logfinite state space. Efficient comparison of the MLSI Dirichlet forms is a wellknown obstacle in the theory of Markov chains. We approach this problem by introducing a regularized MLSI constant, which, under some assumptions, has the same order of magnitude as the usual MLSI constant yet is amenable for comparison and thus considerably simpler to estimate in certain cases. As an application of this general comparison procedure, ...
-
作者：Andres, Sebastian; Gantert, Nina; Schmid, Dominik; Sous, Perla
作者单位：Braunschweig University of Technology; Technical University of Munich; University of Bonn; University of Cambridge
摘要：We study biased random walks on dynamical percolation on Zd. We establish a law of large numbers and an invariance principle for the random walk using regeneration times. Moreover, we verify that the Einstein relation holds, and we investigate the speed of the walk as a function of the bias. While for d = 1 the speed is increasing, we show that, in general, this fails in dimension d >= 2. As our main result, we establish two regimes of parameters, separated by an explicit critical curve such t...
-
作者：Casanova, Adrian Gonzalez; Tobias, Andras; Valesin, Daniel
作者单位：Universidad Nacional Autonoma de Mexico; Budapest University of Technology & Economics; University of Warwick
摘要：We introduce and study an interacting particle system evolving on the ddimensional torus (Z/NZ)d. Each vertex of the torus can be either empty or occupied by an individual of type lambda is an element of (0, infinity). An individual of type lambda dies with rate one and gives birth at each neighboring empty position with rate lambda; moreover, when the birth takes place, the newborn individual is likely to have the same type as the parent but has a small probability of being a mutant. A mutant...
-
作者：Elentano, Michael
作者单位：University of California System; University of California Berkeley
摘要：We develop an approach for studying the local convexity of a certain class of random objectives around the iterates of an AMP algorithm. Our approach involves applying the Sudakov-Fernique inequality conditionally on a long sequence of AMP iterates, and our main contribution is to demonstrate the way in which the resulting objective can be simplified and analyzed. As a consequence, we provide a new, and arguably simpler, proof of some of the results of Celentano, Fan and Mei ( Ann. Statist. 51...
-
作者：Fehrman, Benjamin
作者单位：University of Oxford
摘要：We prove that diffusion equations with a space-time stationary and ergodic, divergence -free drift homogenize in law to a deterministic stochastic partial differential equation with Stratonovich transport noise. In the absence of spatial ergodicity, the drift is only partially absorbed into the skewsymmetric part of the flux through the use of an appropriately defined stream matrix. This leaves a time -dependent, spatially -homogenous transport which, for mildly decorrelating fields, converges...
-
作者：Herry, Ronan; Malicet, Dominique; Poly, Guillaume
作者单位：Universite de Rennes; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We establish, in full generality, an unexpected phenomenon of strong regularization along normal convergence on Wiener chaoses. Namely, for every sequence of chaotic random variables, convergence in law to the Gaussian distribution is automatically upgraded to superconvergence : the regularity of the densities increases along the convergence, and all the derivatives converge uniformly on the real line. Our findings strikingly strengthen known results regarding modes of convergence for normal a...
-
作者：Van Engelenburg, Diederik; Hutchcroft, Tom
作者单位：University of Vienna; California Institute of Technology
摘要：We prove that if a unimodular random rooted graph is recurrent, the number of ends of its uniform spanning tree is almost surely equal to the number of ends of the graph. Together with previous results in the transient case, this completely resolves the problem of the number of ends of wired uniform spanning forest components in unimodular random rooted graphs and confirms a conjecture of Aldous and Lyons (2006).
-
作者：Beliaev, Dmitry; Mcauley, Michael; Muirhead, Stephen
作者单位：University of Oxford; University of Helsinki; University of Melbourne
摘要：3 School of Mathematics and Statistics, University of Melbourne, c smui@unimelb.edu.au For a smooth stationary Gaussian field f on R d and level is an element of R, we consider the number of connected components of the excursion set { f >= } (or level set { f = } ) contained in large domains. The mean of this quantity is known to scale like the volume of the domain under general assumptions on the field. We prove that, assuming sufficient decay of correlations (e.g., the Bargmann-Fock field), ...
