Bouchaud's model exhibits two different aging regimes in dimension one

• 成果类型: Article
• 署名作者: Ben Arous, G; Cerny, J
• 署名单位: New York University; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2005
• 页码: 1161-1192
• 关键词: spin-glasses; CONVERGENCE

摘要

Let E-i be a collection of i.i.d. exponential random variables. Bouchaud's model on Z is a Markov chain X(t) whose transition rates are given by w(ij) = vexp(-beta((1 - a)E-i - aE(j))) if i, j are neighbors in Z. We study the behavior of two correlation functions: P[X(t(w) + t) = X(t(w))] and P[X (t') = X (t(w)) for all t' epsilon [t(w), t(w) + t]]. We prove the (sub)aging behavior of these functions when beta > 1 and a epsilon [0, 1].