Probability Theory and Related Fields

, Volume 134, Issue 1, pp 1-43

First online:

Aging in two-dimensional Bouchaud's model

  • Gérard Ben ArousAffiliated withÉcole Polytechnique, Fédérale de LausanneCourant Institute of Mathematical Sciences Email author 
  • , Jiří ČernýAffiliated withWeierstrass Institute for Applied Analysis and Stochastics (WIAS)
  • , Thomas MountfordAffiliated withDépartement de Mathématiques, École Polytechnique Fédérale de Lausanne

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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.

Key words or phrases

Aging Trap model Lévy process Random walk Time change

Mathematics Subject Classification (2000)

82D30 82C41 60F17