Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Ballistic random walks in random environment at low disorder

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