Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

A law of large numbers for random walks in random mixing environments

Auteur(s):

Code(s) de Classification MSC:

Résumé: We prove a law of large numbers for a class of multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the environment is a weak mixing field in the sense of Dobrushin and Shlosman. Our result holds if the mixing rate balances moments of some random times depending on the path. It applies in the non-nestling case, but we also provide examples of nestling walks that satisfy our assumptions. The derivation is based on an adaptation, using coupling, of the regeneration argument of Sznitman-Zerner.

Mots Clés: Random walk in random environment ; law of large numbers ; Kalikow's condition ; nestling walk ; mixing

Date: 2002-05-29

Prépublication numéro: PMA-733

Postscript file : PMA-733.ps

Pdf file : PMA-733.pdf