WIAS Preprint No. 887, (2003)

Aging in two-dimensional Bouchaud's model


  • Ben Arous, Gerard
  • Cerny, Jiri
  • Mountford, Thomas

2010 Mathematics Subject Classification

  • 82D30 82C41 60F17


  • Aging, trap model, Levy process, random walk, time change


Let E_x be a collection of i.i.d. exponential random variables. Symmetric Bouchaud's model on Z^2 is a Markov chain X(t) whose transition rates are given by w_xy=nu exp(-beta E_x) if x, y are neighbours in Z^2. We study the behaviour of two correlation functions: P[X(t_w+t)=X(t_w)] and P[X(t')=X(t_w)forall t'in[t_w,t_w+t]]. We prove the (sub)aging behaviour of these functions when beta >1.

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