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

Abstract

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 $d\ge 3$.

18 pages. arXiv admin note: text overlap with arXiv:1205.5709 by other authors without attribution

References in corpus (3)

• A survey of random processes with reinforcement
• The Point of View of the Particle on the Law of Large Numbers for Random Walks in a Mixing Random Environment
• Reversed Dirichlet environment and directional transience of random walks in Dirichlet random environment

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