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=νexp(−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].
Citation
Gérard Ben Arous. Jiří Černý. "Bouchaud’s model exhibits two different aging regimes in dimension one." Ann. Appl. Probab. 15 (2) 1161 - 1192, May 2005. https://doi.org/10.1214/105051605000000124
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