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Aging in two-dimensional Bouchaud's model

Ben Arous, Gérard ; Černý, Jiří ; Mountford, Thomas

In: Probability Theory and Related Fields, 2006, vol. 134, no. 1, p. 1-43

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    Titre
    • Aging in two-dimensional Bouchaud's model
    Auteur
    • Ben Arous, Gérard. École Polytechnique, Fédérale de Lausanne, 1015 Lausanne, Switzerland
    • Černý, Jiří. Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, 10117, Berlin, Germany
    • Mountford, Thomas. Département de Mathématiques, École Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Probability Theory and Related Fields, 2006, vol. 134, no. 1, p. 1-43. Springer-Verlag
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:309654
    Summary
    Let E x be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on ℤ2 is a Markov chain X(t) whose transition rates are given by w xy = ν exp (−βE x ) if x, y are neighbours in ℤ2. We study the behaviour of two correlation functions: ℙ[X(t w +t) = X(t w )] and ℙ[X(t') = X(t w ) ∀ t'∈ [t w , t w + t]]. We prove the (sub)aging behaviour of these functions when β > 1