Random walks in a Dirichlet environment

Nathanaël Enriquez, Christophe Sabot

Published 2005-03-30, updated 2005-05-27Version 2

This paper states a law of large numbers for a random walk in a random iid environment on ${\mathbb Z}^d$, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds for the asymptotic velocity of the process and also an asymptotic expansion of this velocity at low disorder.