Bouchaud’s model exhibits two different aging regimes in dimension one
Gérard Ben Arous and Jiří Černý
Source: Ann. Appl. Probab. Volume 15, Number 2
(2005), 1161-1192.
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].
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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1115137972
Digital Object Identifier: doi:10.1214/105051605000000124
Mathematical Reviews number (MathSciNet): MR2134101
Zentralblatt MATH identifier: 1069.60092
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