Sub-ballistic random walk in Dirichlet environment
نویسنده
چکیده
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 characterize directional transience for the initial RWDE. It solves as a corollary the problem of Kalikow’s 0−1 law in the Dirichlet case in any dimension. Furthermore, we find the polynomial order of the magnitude of the original walk’s displacement.
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تاریخ انتشار 2013