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| HAL : hal-00701531, version 1 |
| arXiv : 1205.5709 |
| Fiche détaillée |  Récupérer au format |
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| Sub-ballistic random walk in Dirichlet environment |
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| Élodie Bouchet 1 |
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| (25/05/2012) |
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| 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. |
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| 1 : | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
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| Domaine | : | Mathématiques/Probabilités |
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| Random walk in random environment – Dirichlet distribution – Reinforced random walks – Invariant measure viewed from the particle |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00701531, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00701531 | |
| oai:hal.archives-ouvertes.fr:hal-00701531 | |
| Contributeur : Élodie Bouchet | |
| Soumis le : Vendredi 25 Mai 2012, 16:31:21 | |
| Dernière modification le : Vendredi 25 Mai 2012, 16:36:22 | |
