UNIVERSALITY OF TRAP MODELS IN THE ERGODIC TIME SCALE

• 成果类型: Article
• 署名作者: Jara, M.; Landim, C.; Teixeira, A.
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rouen Normandie
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP886
• 发表日期: 2014
• 页码: 2497-2557
• 关键词: bouchauds model; random-walk; spin-glass; dimension; component; DYNAMICS; rates; graph

摘要

Consider a sequence of possibly random graphs G(N) = (V-N, E-N), N >= 1, whose vertices's have i.i.d. weights {W-x(N) : x is an element of V-N} with a distribution belonging to the basin of attraction of an alpha-stable law, 0 < alpha < 1. Let X-t(N), t >= 0, be a continuous time simple random walk on G(N) which waits a mean W-x(N) exponential time at each vertex x. Under considerably general hypotheses, we prove that in the ergodic time scale this trap model converges in an appropriate topology to a K-process. We apply this result to a class of graphs which includes the hypercube, the d-dimensional torus, d >= 2, random d-regular graphs and the largest component of super-critical Erdos-Renyi random graphs.