no. 3
The quenched invariance principle for random walks in random environments admitting a bounded cycle representation
Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 3, pp. 574-591.

Nous dérivons un principe d'invariance presque sûr pour les marches aléatoires en milieu aléatoire dont les transitions sont données par des poids indexés par des cycles bornés. A cet effet nous adaptons la démonstration pour les marches symétriques en milieu aléatoire de Sidoravicius et Sznitman (Probab. Theory Related Fields 129 (2004) 219-244) dans le cas non réversible.

We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman (Probab. Theory Related Fields 129 (2004) 219-244) to the non-reversible setting.

DOI : 10.1214/07-AIHP122
Classification : 60K37, 60F17
Mots clés : invariance principle, random walks in random environments, non-reversible Markov chains 
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     title = {The quenched invariance principle for random walks in random environments admitting a bounded cycle representation},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {574--591},
     publisher = {Gauthier-Villars},
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     year = {2008},
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Deuschel, Jean-Dominique; Kösters, Holger. The quenched invariance principle for random walks in random environments admitting a bounded cycle representation. Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 3, pp. 574-591. doi : 10.1214/07-AIHP122. http://www.numdam.org/articles/10.1214/07-AIHP122/

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