-
作者：Hermon, Jonathan; Sousi, Perla
作者单位：University of British Columbia; University of Cambridge
摘要：We consider the model of random walk on dynamical percolation introduced by Peres, Stauffer and Steif in (Probab. Theory Related Fields 162 (2015) 487-530). We obtain comparison results for this model for hitting and mixing times and for the spectral gap and log-Sobolev constant with the corresponding quantities for simple random walk on the underlying graph G, for general graphs. When G is the torus Z(n)(d) , we recover the results of Peres et al., and we also extend them to the critical case...
-
作者：Fournier, Nicolas; Tardif, Camille
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：We consider a particle moving in d >= 2 dimensions, its velocity being a reversible diffusion process, with identity diffusion coefficient, of which the invariant measure behaves, roughly, like (1 + vertical bar v vertical bar)(-beta) as vertical bar v vertical bar -> infinity, for some constant beta > 0. We prove that for large times, after a suitable rescaling, the position process resembles a Brownian motion if beta >= 4 + d, a stable process if beta is an element of [d, 4 + d) and an integ...
-
作者：Spinka, Yinon
作者单位：University of British Columbia
摘要：It has been shown by van den Berg and Steif (Ann. Probab. 27 (1999) 1501-1522) that the subcritical and critical Ising model on Z(d) is a finitary factor of an i.i.d. process (ffiid), whereas the super-critical model is not. In fact, they showed that the latter is a general phenomenon in that a phase transition presents an obstruction for being ffiid. The question remained whether this is the only such obstruction. We make progress on this, showing that certain spatial mixing conditions (notio...
-
作者：Flandoli, Franco; Luo, Dejun
作者单位：Scuola Normale Superiore di Pisa; Chinese Academy of Sciences
摘要：We consider the vorticity form of the 2D Euler equations which is perturbed by a suitable transport type noise and has white noise initial condition. It is shown that stationary solutions of this equation converge to the unique stationary solution of the 2D Navier-Stokes equation driven by the space-time white noise.
-
作者：Hermon, Jonathan; Pymar, Richard
作者单位：University of British Columbia; University of London; Birkbeck University London
摘要：Oliveira conjectured that the order of the mixing time of the exclusion process with k-particles on an arbitrary n-vertex graph is at most that of the mixing-time of k independent particles. We verify this up to a constant factor for d-regular graphs when each edge rings at rate 1/d in various cases: (1) when d = Omega (log(n/k)n), (2) when gap := the spectral-gap of a single walk is O (1/log(4) n) and k >= n(Omega(1)), (3) when k asymptotic to n(a) for some constant 0 < a < 1. In these cases,...
-
作者：Lacker, Daniel; Shkolnikov, Mykhaylo; Zhang, Jiacheng
作者单位：Columbia University; Princeton University
摘要：We study two-dimensional stochastic differential equations (SDEs) of McKean-Vlasov type in which the conditional distribution of the second component of the solution given the first enters the equation for the first component of the solution. Such SDEs arise when one tries to invert the Markovian projection developed in (Probab. Theory Related Fields 71 (1986) 501-516), typically to produce an Ito process with the fixed-time marginal distributions of a given one-dimensional diffusion but riche...
-
作者：Loehr, Wolfgang; Mytnik, Leonid; Winter, Anita
作者单位：University of Duisburg Essen; Technion Israel Institute of Technology
摘要：In (Combin. Probab. Comput. 9 (2000) 191-204), Aldous investigates a symmetric Markov chain on cladograms and gives bounds on its mixing and relaxation times. The latter bound was sharpened in (Random Structures Algorithms 20 (2002) 59-70). In the present paper, we encode cladograms as binary, algebraic measure trees and show that this Markov chain on cladograms with a fixed number of leaves converges in distribution as the number of leaves tends to infinity. We give a rigorous construction of...
-
作者：Hutchcroft, Tom
作者单位：University of Cambridge
摘要：Around 2008, Schramm conjectured that the critical probabilities for Bernoulli bond percolation satisfy the following continuity property: If (G(n))(n >= 1) is a sequence of transitive graphs converging locally to a transitive graph G and lim sup(n ->infinity) pc(G(n)) < 1, then p(c)(G(n)) -> p(c)(G) as n -> infinity. We verify this conjecture under the additional hypothesis that there is a uniform exponential lower bound on the volume growth of the graphs in question. The result is new even i...
-
作者：Janvresse, Elise; Roy, Emmanuel; de la Rue, Thierry
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Picardie Jules Verne (UPJV); Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); Universite de Rouen Normandie
摘要：In this paper, we study splittings of a Poisson point process which are equivariant under a conservative transformation. We show that, if the Cartesian powers of this transformation are all ergodic, the only ergodic splitting is the obvious one, that is, a collection of independent Poisson processes. We apply this result to the case of a marked Poisson process: under the same hypothesis, the marks are necessarily independent of the point process and i.i.d. Under additional assumptions on the t...
-
作者：Kopel, Phil; Orourke, Sean; Vu, Van
作者单位：University of Colorado System; University of Colorado Boulder; Yale University
摘要：We establish, under a moment matching hypothesis, the local universality of the correlation functions associated with products of M independent i.i.d. random matrices, as M is fixed, and the sizes of the matrices tend to infinity. This generalizes an earlier result of Tao and the third author for the case M = 1. We also prove Gaussian limits for the centered linear spectral statistics of products of M independent i.i.d. random matrices. This is done in two steps. First, we establish the result...
