Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

On the limiting velocity of random walks in mixing random environment

Xiaoqin Guo

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Abstract

We consider random walks in strong-mixing random Gibbsian environments in $\mathbb{Z}^{d}$, $d\ge2$. Based on regeneration arguments, we will first provide an alternative proof of Rassoul-Agha’s conditional law of large numbers (CLLN) for mixing environment (Electron. Commun. Probab. 10 (2005) 36–44). Then, using coupling techniques, we show that there is at most one nonzero limiting velocity in high dimensions ($d\ge5$).

Résumé

Nous considérons des marches aléatoires dans un environnement Gibbsien fortement mélangeant dans $\mathbb{Z}^{d}$, $d\ge2$. A l’aide d’arguments de renouvellement, nous donnons d’abord une preuve alternative de la loi conditionnelle des grands nombres de Rassoul-Agha (Electron. Commun. Probab. 10 (2005) 36–44) pour des environnements mélangeants. Ensuite, par des méthodes de couplage, nous montrons qu’il existe au plus une vitesse limite non nulle en grande dimension ($d\ge5$).

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 50, Number 2 (2014), 375-402.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1395856132

Digital Object Identifier
doi:10.1214/12-AIHP534

Mathematical Reviews number (MathSciNet)
MR3189076

Zentralblatt MATH identifier
1291.60211

Subjects
Primary: 60K37: Processes in random environments

Keywords
Random walks Random environment Mixing Limiting speed Conditional law of large numbers

Citation

Guo, Xiaoqin. On the limiting velocity of random walks in mixing random environment. Ann. Inst. H. Poincaré Probab. Statist. 50 (2014), no. 2, 375--402. doi:10.1214/12-AIHP534. https://projecteuclid.org/euclid.aihp/1395856132


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