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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60K40 Other physical applications of random processes
- 82D30 Random media, disordered materials (including liquid crystals and spin glasses)

**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