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

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

Gaussian fluctuations for random walks in random mixing environments


Code(s) de Classification MSC:

Résumé: We consider a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions. Continuing our previous work [2] for the law of large numbers, we prove here that the fluctuations are gaussian when the environment is Gibbsian satisfying the "strong mixing condition" of Dobrushin and Shlosman and the mixing rate is large enough to balance moments of some random times depending on the path. Under appropriate assumptions the CLT applies in both non-nestling and nestling cases, and trivialy in the case of finite-dependent environments with "strong enough bias". Our proof makes use of the asymptotic regeneration scheme introduced in [2]. When the environment is only weakly mixing, we can only prove that if the fluctuations are diffusive then they are necessarily Gaussian.

Mots Clés: Random walk in random environment ; central limit theorem ; Kalikow's condition ; nestling walk ; mixing ; renewal ; regeneration

Date: 2004-02-24

Prépublication numéro: PMA-883