Bouchaud’s model exhibits two different aging regimes in dimension one

Arous, Gérard Ben; Černý, Jiří

Ann. Appl. Probab., Tome 15 (2005) no. 1A, p. 1161-1192 / Harvested from Project Euclid

Résumé

Let E_i be a collection of i.i.d. exponential random variables. Bouchaud’s model on ℤ is a Markov chain X(t) whose transition rates are given by w_ij=νexp(−β((1−a)E_i−aE_j)) if i, j are neighbors in ℤ. We study the behavior 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 behavior of these functions when β>1 and a∈[0,1].

Publié le : 2005-05-14
Classification: Aging, singular diffusions, random walk in random environment, Lévy processes, 60K37, 82C44, 60G18, 60F17

@article{1115137972,
     author = {Arous, G\'erard Ben and \v Cern\'y, Ji\v r\'\i },
     title = {Bouchaud's model exhibits two different aging regimes in dimension one},
     journal = {Ann. Appl. Probab.},
     volume = {15},
     number = {1A},
     year = {2005},
     pages = { 1161-1192},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1115137972}
}

Arous, Gérard Ben; Černý, Jiří. Bouchaud’s model exhibits two different aging regimes in dimension one. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp.  1161-1192. http://gdmltest.u-ga.fr/item/1115137972/