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Aging in two-dimensional Bouchaud's model |
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| Authors: | Gérard Ben Arous Jiří Černý Thomas Mountford |
| Affiliation: | (1) école Polytechnique, Fédérale de Lausanne, 1015 Lausanne, Switzerland;(2) Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, N.Y. 10012-1185, USA;(3) Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, 10117 Berlin, Germany;(4) Département de Mathématiques, école Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland |
| Abstract: | 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. |
| Keywords: | Aging Trap model Lévy process Random walk Time change |
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