The Annals of Applied Probability

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

Gérard Ben Arous and Jiří Černý

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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)EiaEj)) 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].

Article information

Ann. Appl. Probab. Volume 15, Number 2 (2005), 1161-1192.

First available: 3 May 2005

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Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments 82C44: Dynamics of disordered systems (random Ising systems, etc.) 60G18: Self-similar processes
Secondary: 60F17: Functional limit theorems; invariance principles

Aging singular diffusions random walk in random environment Lévy processes


Arous, Gérard Ben; Černý, Jiří. Bouchaud’s model exhibits two different aging regimes in dimension one. The Annals of Applied Probability 15 (2005), no. 2, 1161--1192. doi:10.1214/105051605000000124.

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