2177 articles – 2572 references  [version française]
 HAL: hal-00701531, version 1
 arXiv: 1205.5709
 Sub-ballistic random walk in Dirichlet environment
 (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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 hal-00701531, version 1 http://hal.archives-ouvertes.fr/hal-00701531 oai:hal.archives-ouvertes.fr:hal-00701531 From: Élodie Bouchet <> Submitted on: Friday, 25 May 2012 16:31:21 Updated on: Friday, 25 May 2012 16:36:22