Aging in two-dimensional Bouchaud's model

Abstract

Let E x be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on ℤ2 is a Markov chain X(t) whose transition rates are given by w xy = ν exp (-βE x ) if x, y are neighbours in ℤ2. We study the behaviour of two correlation functions: ℙ[X(t w +t) = X(t w )] and ℙ[X(t') = X(t w ) ∀ t' [tw , tw + t]]. We prove the (sub)aging behaviour of these functions when β > 1.