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

Abstract

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=νexp(−β((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) ∀ t'∈[t_w,t_w+t]]. We prove the (sub)aging behavior of these functions when β>1 and a∈[0,1].