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:**

- 60K37 Processes in random environments
- 82D30 Random media, disordered materials (including liquid crystals and spin glasses)
- 60F05 Central limit and other weak theorems

**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*