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

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

2002-10-29

arxiv.org/abs/cond-mat/0210633v3

Annals of Applied Probability 2005, Vol. 15, No. 2, 1161-1192

Physics

Condensed Matter

Published at http://dx.doi.org/10.1214/105051605000000124 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051605000000124

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}=\nu \exp(-\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) \forall t'\in[t_w,t_w+t]]. We prove the (sub)aging behavior of these functions when \beta >1 and a\in[0,1].

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