Random Dirichlet environment viewed from the particle in dimension $d\ge 3$

Christophe Sabot (1)

1 ICJ - Institut Camille Jordan

We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On ${\mathbb Z}^d$, RWDE are parameterized by a $2d$-uplet of positive reals called weights. In this paper, we characterize for $d\ge 3$ the weights for which there exists an absolutely continuous invariant probability for the process viewed from the particle. We can deduce from this result and from [27] a complete description of the ballistic regime for $d\ge 3$.

Mots clés: Random walk in random environment; Dirichlet distribution; Reinforced random walks; invariant measure viewed from the particle

Domaines: Probabilités [math.PR]

Christophe Sabot. Random Dirichlet environment viewed from the particle in dimension $d\ge 3$. Annals of Probability, 2013, 41 (2), pp.722-743. ⟨10.1214/11-AOP699⟩. ⟨hal-00502707v3⟩