Random Dirichlet environment viewed from the particle in dimension d≥ 3

الأصل · EN

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 Zᵈ, RWDE are parameterized by a 2d-uplet of positive reals called weights. In this paper, we characterize for d≥ 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≥ 3.