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

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

2010-07-15

arxiv.org/abs/1007.2565v2

Mathematics

Probability

18 pages

Scientific paper

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 $d\ge 3$.

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