Bouchaud's model exhibits two different aging regimes in dimension one
Abstract
Let Ei 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 wij=ν(-β((1-a)Ei-aEj)) if i, j are neighbors in Z. We study the behavior of two correlation functions: P[X(tw+t)=X(tw)] and P[X(t')=X(tw) ∀ t'∈[tw,tw+t]]. We prove the (sub)aging behavior of these functions when β>1 and a∈[0,1].
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