Probability Theory and Related Fields

, Volume 134, Issue 1, pp 1–43

Aging in two-dimensional Bouchaud's model

  • Gérard Ben Arous
  • Jiří Černý
  • Thomas Mountford

DOI: 10.1007/s00440-004-0408-1

Cite this article as:
Ben Arous, G., Černý, J. & Mountford, T. Probab. Theory Relat. Fields (2006) 134: 1. doi:10.1007/s00440-004-0408-1


Let Ex 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 wxy = ν exp (−βEx) if x, y are neighbours in ℤ2. We study the behaviour 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 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 

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Gérard Ben Arous
    • 1
    • 2
  • Jiří Černý
    • 3
  • Thomas Mountford
    • 4
  1. 1.École PolytechniqueFédérale de LausanneSwitzerland
  2. 2.Courant Institute of Mathematical SciencesNew YorkUSA
  3. 3.Weierstrass Institute for Applied Analysis and Stochastics (WIAS)BerlinGermany
  4. 4.Département de MathématiquesÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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