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

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).

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).

DOI : https://doi.org/10.1214/12-AIHP534
Classification:  60K37
Keywords: random walks, random environment, mixing, limiting speed, conditional law of large numbers
@article{AIHPB_2014__50_2_375_0,
     author = {Guo, Xiaoqin},
     title = {On the limiting velocity of random walks in mixing random environment},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {2},
     year = {2014},
     pages = {375-402},
     doi = {10.1214/12-AIHP534},
     zbl = {1291.60211},
     mrnumber = {3189076},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2014__50_2_375_0}
}
Guo, Xiaoqin. On the limiting velocity of random walks in mixing random environment. Annales de l'I.H.P. Probabilités et statistiques, Volume 50 (2014) no. 2, pp. 375-402. doi : 10.1214/12-AIHP534. http://www.numdam.org/item/AIHPB_2014__50_2_375_0/

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