Aging in two-dimensional Bouchaud's model

Gérard Ben Arous, Jiří Černý, Thomas Mountford

Research output: Contribution to journalArticlepeer-review

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' [tw , tw + t]]. We prove the (sub)aging behaviour of these functions when β > 1.

Original languageEnglish (US)
Pages (from-to)1-43
Number of pages43
JournalProbability Theory and Related Fields
Volume134
Issue number1
DOIs
StatePublished - Jan 2006

Keywords

  • Aging
  • Lévy process
  • Random walk
  • Time change
  • Trap model

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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