-
作者：Bramson, M; Liggett, TM
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of California System; University of California Los Angeles
摘要：There has been significant progress recently in our understanding of the stationary measures of the exclusion process on Z. The corresponding situation in higher dimensions remains largely a mystery. In this paper we give necessary and sufficient conditions for a product measure to be stationary for the exclusion process on an arbitrary set, and apply this result to find examples on Z(d) and on homogeneous trees in which product measures are stationary even when they are neither homogeneous no...
-
作者：Durrett, R; Schweinsberg, J
作者单位：Cornell University; University of California System; University of California San Diego
摘要：Qian, Luscombe and Gerstein [J. Molecular Biol. 313 (2001) 673-681] introduced a model of the diversification of protein folds in a genome that we may formulate as follows. Consider a multitype Yule process starting with one individual in which there are no deaths and each individual gives birth to a new individual at rate 1. When a new individual is born, it has the same type as its parent with probability 1 - r and is a new type, different from all previously observed types, with probability...
-
作者：Kesten, H; Sidoravicius, V
作者单位：Cornell University
摘要：We consider the following interacting particle system: There is a gas of particles, each of which performs a continuous-time simple random walk on Z(d), with jump rate D-A. These particles are called A-particles and move independently of each other. They are regarded as individuals who are ignorant of a rumor or are healthy. We assume that we start the system with N-A (X, 0-) A-particles at x, and that the N-A (X, 0-), x epsilon Z(d), are i.i.d., mean-mu(A) Poisson random variables. In additio...
-
作者：Merkl, F; Rolles, SWW
作者单位：University of Munich; University of Bielefeld
摘要：We prove that the edge-reinforced random walk on the ladder Z x 11, 21 with initial weights a > 3/4 is recurrent. The proof uses a known representation of the edge-reinforced random walk on a finite piece of the ladder as a random walk in a random environment. This environment is given by a marginal of a multicomponent Gibbsian process. A transfer operator technique and entropy estimates from statistical mechanics are used to analyze this Gibbsian process. Furthermore, we prove spatially expon...
-
作者：Duquesne, T
作者单位：Universite Paris Saclay
摘要：Let b be an integer greater than I and let W-epsilon = (W-n(epsilon); n > 0) be a random walk on the b-ary rooted tree U-b, starting at the root, going up (resp. down) with probability 1/2 + epsilon (resp. 1/2 - epsilon), epsilon is an element of (0, 1/2), and choosing direction i epsilon {1,...,b) when going up with probability a(i). Here a = (a(1),...,a(b)) stands for some nondegenerated fixed set of weights. We consider the range {W-n(epsilon); n >= 0} that is a subtree Of U-b. It correspon...
-
作者：Andjel, ED; Guiol, H
作者单位：Aix-Marseille Universite; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble
摘要：We show that if mu is an invariant measure for the long range exclusion process putting no mass on the full configuration, L is the formal generator of that process and f is a cylinder function, then Lf is an element of L-1 (d mu) and integral Lf d mu = 0. This result is then applied to determine (i) the set of invariant and translation-invariant measures of the long range exclusion process on Z(d) when the underlying random walk is irreducible; (ii) the set of invariant measures of the long r...
-
作者：Pitman, J; Winkel, M
作者单位：University of California System; University of California Berkeley; University of Oxford
摘要：Trees in Brownian excursions have been studied since the late 1980s. Forests in excursions of Brownian motion above its past minimum are a natural extension of this notion. In this paper we study a forest-valued Markov process which describes the growth of the Brownian forest. The key result is a composition rule for binary Galton-Watson forests with i.i.d. exponential branch lengths. We give elementary proofs of this composition rule and explain how it is intimately linked with Williams' deco...
-
作者：Ben Arous, G; Molchanov, S; Ramírez, AF
作者单位：New York University; University of North Carolina; University of North Carolina Charlotte; Pontificia Universidad Catolica de Chile
摘要：In this work we study a natural transition mechanism describing the passage from a quenched (almost sure) regime to an annealed (in average) one, for a symmetric simple random walk on random obstacles on sites having an identical and independent law. The transition mechanism we study was first proposed in the context of sums of identical independent random exponents by Ben Arous, Bogachev and Molchanov in [Probab. Theory Related Fields 132 (2005) 579-612]. Let p(x, t) be the survival probabili...
-
作者：Pra, PD; Posta, G
作者单位：University of Padua; Polytechnic University of Milan
摘要：We prove that the logarithmic Sobolev constant for zero-range processes in a box of diameter L grows as L-2.
-
作者：Schramm, O; Sheffield, S
作者单位：Microsoft; University of California System; University of California Berkeley
摘要：The harmonic explorer is a random grid path. Very roughly, at each step the harmonic explorer takes a turn to the right with probability equal to the discrete harmonic measure of the left-hand side of the path from a point near the end of the current path. We prove that the harmonic explorer converges to SLE4 as the grid gets finer.
