Excited random walk is a model of a random walk on Z which, whenever it encounters a new vertex it receives a push toward a specific direction, call it the “right”, while when it reaches a vertex it “already knows”, it performs a simple random walk. This model has been suggested in [BW] and had since got lots of attention, see [V, Z]. The reason for the interest is that it is situated very natu...

Abstract. We consider random walks in Dirichlet environment (RWDE) on Z, for d > 3, in the sub-ballistic case. We associate to any parameter (α1, . . . , α2d) of the Dirichlet law a time-change to accelerate the walk. We prove that the continuoustime accelerated walk has an absolutely continuous invariant probability measure for the environment viewed from the particle. This allows to character...

In this paper we are interested in Sinai’s walk i.e a one dimensional random walk in random environment with three conditions on the random environment: two necessaries hypothesis to get a recurrent process (see [Solomon(1975)]) which is not a simple random walk and an hypothesis of regularity which allows us to have a good control on the fluctuations of the random environment. The asymptotic b...

In this paper we are interested in Sinai’s walk i.e., a one dimensional random walk in random environment with three conditions on the random environment: two necessaries hypothesis to get a recurrent process (see [Solomon(1975)]) which is not a simple random walk and an hypothesis of regularity which allows us to have a good control on the fluctuations of the random environment. The asymptotic...