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)
- 82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.)

**Résumé:** We consider random walks in a
random environment of the type $p_0+\gamma\w_z$, where $p_0$
denotes the transition probabilities of a stationary random walk
on $\BZ^d$, to nearest neighbors, and $\w_z$ is an iid random
perturbation. We give an explicit development, for small
$\gamma$, of the asymptotic speed of the random walk under the
annealed law, up to order 2. As an application, we construct, in
dimension $d\ge 2$, a walk which goes faster than the stationary
walk under the mean environment.

**Mots Clés:** *Random walks ; random media ; random walks in random environment*

**Date:** 2003-02-07

**Prépublication numéro:** *PMA-790*