Sub-ballistic random walk in Dirichlet environment

2012/05/25 by Bouchet, Élodie
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1205.5709

Abstract

We consider random walks in Dirichlet environment (RWDE) on \Z ^d, for d ≥ 3 , in the sub-ballistic case. We associate to any parameter (α₁, ..., α_2d) of the Dirichlet law a time-change to accelerate the walk. We prove that the continuous-time 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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