Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

The quenched invariance principle for random walks in random environments admitting a bounded cycle representation

Jean-Dominique Deuschel and Holger Kösters

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Abstract

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.

Résumé

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.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 44, Number 3 (2008), 574-591.

Dates
First available in Project Euclid: 26 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1211819425

Digital Object Identifier
doi:10.1214/07-AIHP122

Mathematical Reviews number (MathSciNet)
MR2451058

Zentralblatt MATH identifier
1176.60085

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60F17: Functional limit theorems; invariance principles

Keywords
Invariance principle Random walks in random environments Non-reversible Markov chains

Citation

Deuschel, Jean-Dominique; Kösters, Holger. The quenched invariance principle for random walks in random environments admitting a bounded cycle representation. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), no. 3, 574--591. doi:10.1214/07-AIHP122. https://projecteuclid.org/euclid.aihp/1211819425


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