Publication date
January 2005
DOI Publisher
Springer Science and Business Media LLCAbstract
Let \tau_x be a collection of i.i.d. positive random variables with distribution in the domain of attraction of \alpha-stable law with \alpha <1. The symmetric Bouchaud's trap model on Z is a Markov chain X(t) whose transition rates are given by w_{xy}=(2\tau_x)^{-1} if x, y are neighbours in Z. We study the behaviour 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]]. It is well known that for any of these correlation functions a time-scale t=f(t_w) such that aging occurs can be found. We study these correlation functions on time-scales different from f(t_w), and we describe more precisely the behaviour of a singular diffusion obtained as the scaling limit of Bouchaud's trap model
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