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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...
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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...
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作者：Miclo, Laurent; Patie, Pierre; Sarkar, Rohan
作者单位：Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Cornell University
摘要：The first aim of this paper is to introduce a class of Markov chains on Z(+) which are discrete self-similar in the sense that their semigroups satisfy an in-variance property expressed in terms of a discrete random dilation operator. After showing that this latter property requires the chains to be upward skip-free, we first establish a gateway intertwining relation between the semigroup of such chains and the one of spectrally negative self-similar Markov pro-cesses on R+. As a by-product, w...
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作者：Liu, Zhipeng
作者单位：University of Kansas
摘要：Recently Johansson and Rahman obtained the limiting multitime distribution for the discrete polynuclear growth model (Johansson and Rahman (2019)), which is equivalent to a discrete TASEP model with step initial condition. In this paper, we obtain a finite time multipoint distribution formula of continuous TASEP with general initial conditions in the space-time plane. We evaluate the limit of this distribution function when the times go to infinity at the same speed for both step and flat init...
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作者：Ioffe, Dmitry; Ott, Sebastien; Shlosman, Senya; Velenik, Yvan
作者单位：Technion Israel Institute of Technology; Roma Tre University; University of Geneva
摘要：In this paper, we develop a detailed analysis of critical prewetting in the context of the two-dimensional Ising model. Namely, we consider a two-dimensional nearest-neighbor Ising model in a 2N x N rectangular box with a boundary condition inducing the coexistence of the + phase in the bulk and a layer of - phase along the bottom wall. The presence of an external magnetic field of intensity h = lambda/N (for some fixed lambda > 0) makes the layer of - phase unstable. For any beta > beta(c), w...
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作者：Cerrai, Sandra; Xi, Guangyu
作者单位：University System of Maryland; University of Maryland College Park
摘要：We study the validity of a Smoluchowski-Kramers approximation for a class of wave equations in a bounded domain of R-n subject to a state-dependent damping and perturbed by a multiplicative noise. We prove that in the small mass limit the solution converges to the solution of a stochastic quasilinear parabolic equation where a noise-induced extra drift is created.
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作者：Fitzgerald, Will; Tribe, Roger; Zaboronski, Oleg
作者单位：University of Manchester; University of Warwick
摘要：Motivated by the phenomenon of duality for interacting particle systems, we introduce two classes of Pfaffian kernels describing a number of Pfaf-fian point processes in the bulk and at the edge. Using the probabilistic method due to Mark Kac, we prove two Szego-type asymptotic expansion theorems for the corresponding Fredholm Pfaffians. The idea of the proof is to introduce an effective random walk with transition density determined by the Pfaffian kernel, express the logarithm of the Fredhol...
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作者：Borga, Jacopo; Maazoun, Mickael
作者单位：University of Zurich; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：Baxter permutations, plane bipolar orientations, and a specific family of walks in the nonnegative quadrant, called tandem walks, are well-known to be related to each other through several bijections. We introduce a further new family of discrete objects, called coalescent-walk processes and we relate it to the three families mentioned above. We prove joint Benjamini-Schramm convergence (both in the annealed and quenched sense) for uniform objects in the four families. Furthermore, we explicit...
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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...
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作者：Dyszewski, Piotr; Gantert, Nina; Johnston, Samuel G. G.; Prochno, Joscha; Schmid, Dominik
作者单位：Technical University of Munich; University of Bath; University of Passau
摘要：We study the asymptotics of the k-regular self-similar fragmentation process. For alpha > 0 and an integer k >= 2, this is the Markov process (I-t)(t >= 0) in which each I-t is a union of open subsets of [0, 1), and independently each subinterval of I-t of size u breaks into k equally sized pieces at rate u(alpha). Let k(-mt) and k(-Mt) be the respective sizes of the largest and smallest fragments in I-t. By relating (I-t)(t >= 0) to a branching random walk, we find that there exist explicit d...
