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作者：Blanquicett, Daniel
作者单位：University of California System; University of California Davis
摘要：Consider a p-random subset A of initially infected vertices in the discrete cube [L](3), and assume that the neighborhood of each vertex consists of the a(i) nearest neighbors in the +/- e(i)-directions for each i is an element of {1, 2, 3}, where a(1) <= a(2) <= a(3). Suppose we infect any healthy vertex x is an element of [L](3) already having a(3) + 1 infected neighbors, and that infected sites remain infected forever. In this paper, we determine the critical length for percolation up to a ...
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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...
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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...
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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...
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作者：Augeri, Fanny
作者单位：Weizmann Institute of Science
摘要：We prove general nonlinear large deviation estimates similar to Chatterjee-Dembo's original bounds, except that we do not require any second order smoothness. Our approach relies on convex analysis arguments and is valid for a broad class of distributions. Our results are then applied in three different setups. Our first application consists in the mean-field approximation of the partition function of the Ising model under an optimal assumption on the spectra of the adjacency matrices of the s...
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作者：Nica, Mihai; Quastel, Jeremy; Remenik, Daniel
作者单位：University of Toronto; Universidad de Chile; Universidad de Chile
摘要：We provide a direct and elementary proof that the formula obtained in (Matetski, Quastel and Remenik (2016)) for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov backward equation. The same method yields the solution for the related PushASEP particle system.
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作者：Backhoff-Veraguas, Julio; Beiglboeck, Mathias; Huesmann, Martin; Kallblad, Sigrid
作者单位：University of Twente; University of Vienna; Royal Institute of Technology
摘要：In classical optimal transport, the contributions of Benamou-Brenier and McCann regarding the time-dependent version of the problem are corner-stones of the field and form the basis for a variety of applications in other mathematical areas. We suggest a Benamou-Brenier type formulation of the martingale transport problem for given d-dimensional distributions mu, nu in convex order. The unique solution M* = (M-t*)(t is an element of[0,1]) of this problem turns out to be a Markov-martingale whic...
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作者：Komorowski, Tomasz; Olla, Stefano; Ryzhik, Lenya
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Stanford University
摘要：We consider the limit of a linear kinetic equation with reflection-transmission-absorption at an interface and with a degenerate scattering kernel. The equation arises from a microscopic chain of oscillators in contact with a heat bath. In the absence of the interface, the solutions exhibit a superdiffusive behavior in the long time limit. With the interface, the long time limit is the unique solution of a version of the fractional in space heat equation with reflection-transmission-absorption...
