On the limiting velocity of random walks in mixing random environment
Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 2, pp. 375-402.

Nous considérons des marches aléatoires dans un environnement Gibbsien fortement mélangeant dans d , d2. 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 (d5).

We consider random walks in strong-mixing random Gibbsian environments in d , d2. 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 (d5).

DOI : 10.1214/12-AIHP534
Classification : 60K37
Mots clés : random walks, random environment, mixing, limiting speed, conditional law of large numbers
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Guo, Xiaoqin. On the limiting velocity of random walks in mixing random environment. Annales de l'I.H.P. Probabilités et statistiques, Tome 50 (2014) no. 2, pp. 375-402. doi : 10.1214/12-AIHP534. http://www.numdam.org/articles/10.1214/12-AIHP534/

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