-
作者：de Raphelis, Loic
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We consider a random walk on a Galton-Watson tree in random environment, in the subdiffusive case. We prove the convergence of the renormalised height function of the walk towards the continuous-time height process of a spectrally positive strictly stable Levy process, jointly with the convergence of the renormalised trace of the walk towards the real tree coded by the latter continuous-time height process.
-
作者：Bednorz, Witold; Martynek, Rafal
作者单位：University of Warsaw
摘要：In this paper we complete the full characterization of the expected suprema of infinitely divisible processes. In particular, we remove the technical assumption called H(C-0, delta) condition and settle positively the conjecture posed by M. Talagrand.
-
作者：Dauvergne, Duncan
作者单位：Princeton University
摘要：Last passage percolation and directed polymer models on Z(2) are invariant under translation and certain reflections. When these models have an integrable structure coming from either the RSK correspondence or the geometric RSK correspondence (e.g., geometric last passage percolation or the log-gamma polymer), we show that these basic invariances can be combined with a decoupling property to yield a rich new set of symmetries. Among other results, we prove shift and rearrangement invariance st...
-
作者：Forghani, Behrang; Tiozzo, Giulio
作者单位：College of Charleston; University of Toronto
摘要：We establish the ray and strip approximation criteria for the identification of the Poisson boundary of random walks on locally compact groups. This settles a conjecture from the 1990s by Kaimanovich, who formulated and proved the criterion for discrete groups. The key result is the proof of a version of the Shannon-McMillan-Breiman theorem for locally compact groups. We provide several applications to locally compact groups of isometrics of nonpositively curved spaces, as well as Diestel-Lead...
-
作者：Shen, Hao; Smith, Scott A.; Zhu, Rongchan; Zhu, Xiangchan
作者单位：University of Wisconsin System; University of Wisconsin Madison; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Beijing Institute of Technology
摘要：This article studies large N limits of a coupled system of N interacting Phi(4) equations posed over T-d for d = 2, known as the O(N) linear sigma model. Uniform in N bounds on the dynamics are established, allowing us to show convergence to a mean-field singular SPDE, also proved to be globally well posed. Moreover, we show tightness of the invariant measures in the large N limit. For large enough mass, they converge to the (massive) Gaussian free field, the unique invariant measure of the me...
-
作者：Bedrossian, Jacob; Blumenthal, Alex; Punshon-Smith, Samuel
作者单位：University System of Maryland; University of Maryland College Park; Brown University
摘要：We deduce almost-sure exponentially fast mixing of passive scalars advected by solutions of the stochastically-forced 2D Navier-Stokes equations and 3D hyper-viscous Navier-Stokes equations in T-d subjected to nondenegenerate H-sigma-regular noise for any sigma sufficiently large. That is, for all s > 0 there is a deterministic exponential decay rate such that all mean-zero H-s passive scalars decay in H-s at this same rate with probability one. This is equivalent to what is known as quenched ...
-
作者：Chatterjee, Sourav; Diaconis, Persi; Sly, Allan; Zhang, Lingfu
作者单位：Stanford University; Stanford University; Princeton University
摘要：Let x(1), ..., x(n) be a fixed sequence of real numbers. At each stage, pick two indices I and J uniformly at random, and replace x(I), x(J) by (x(I) +x(J))/2, (x(I) +x(J))/2. Clearly, all the coordinates converge to (x(1)+ ...+ x(n))/n. We determine the rate of convergence, establishing a sharp cutoff transition answering a question of Jean Bourgain.
-
作者：Conchon-Kerjan, Guillaume
作者单位：Universite Paris Cite
摘要：We prove the cutoff phenomenon for the random walk on random n-lifts of finite weighted graphs, even when the random walk on the base graph c of the lift is not reversible. The mixing time is w.h.p. t(mix) = h(-1) log n, where h is a constant associated to G, namely the entropy of its universal cover. Moreover, this mixing time is the smallest possible among all n-lifts of G. In the particular case where the base graph is a vertex with d/2 loops, d even, we obtain a cutoff for a d-regular rand...
-
作者：Hermon, Jonathan; Sly, Allan; Sousi, Perla
作者单位：University of British Columbia; Princeton University; University of Cambridge
摘要：We establish universality of cutoff for simple random walk on a class of random graphs defined as follows. Given a finite graph G = (V, E) with vertical bar V vertical bar even we define a random graph G* = (V, E U E') obtained by picking E' to be the (unordered) pairs of a random perfect matching of V. We show that for a sequence of such graphs G(n) of diverging sizes and of uniformly bounded degree, if the minimal size of a connected component of G(n) is at least 3 for all n, then the random...
-
作者：Busani, Ofer; Ferrari, Patrik L.
作者单位：University of Bristol; University of Bonn
摘要：In this paper, we consider the geodesic tree in exponential last passage percolation. We show that for a large class of initial conditions around the origin, the line-to-point geodesic that terminates in a cylinder located around the point (N, N), and whose width and length are o(N-2/3) and o(N), respectively, agrees in the cylinder, with the stationary geodesic sharing the same end-point. In the case of the point-to-point model where the geodesic starts from the origin, we consider width delt...
