HAL: hal-00701531, version 1

arXiv: 1205.5709

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Sub-ballistic random walk in Dirichlet environment

Élodie Bouchet 1

(2012-05-25)

We consider random walks in Dirichlet environment (RWDE) on $\Z ^d$, for $ d \geq 3 $, in the sub-ballistic case. We associate to any parameter $ (\alpha_1, \dots, \alpha _{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.

1:	Institut Camille Jordan (ICJ)
	CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon

Subject

:

Mathematics/Probability

Keyword(s): Random walk in random environment – Dirichlet distribution – Reinforced random walks – Invariant measure viewed from the particle

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From: Élodie Bouchet <>

Submitted on: Friday, 25 May 2012 16:31:21

Updated on: Friday, 25 May 2012 16:36:22