A quenched functional central limit theorem for random walks in random environments under (T)γ

Élodie Bouchet, Christophe Sabot and Renato Soares dos Santos

Stochastic Processes and their Applications, 2016, vol. 126, issue 4, 1206-1225

Abstract: We prove a quenched central limit theorem for random walks in i.i.d. weakly elliptic random environments in the ballistic regime. Such theorems have been proved recently by Rassoul-Agha and Seppäläinen in Rassoul-Agha and Seppäläinen (2009) and Berger and Zeitouni in Berger and Zeitouni (2008) under the assumption of large finite moments for the regeneration time. In this paper, with the extra (T)γ condition of Sznitman we reduce the moment condition to E(τ2(lnτ)1+m)<+∞ for m>1+1/γ, which allows the inclusion of new non-uniformly elliptic examples such as Dirichlet random environments.

Keywords: Random walk in random environment; Quenched central limit theorem; Ballisticity condition (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:4:p:1206-1225

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DOI: 10.1016/j.spa.2015.10.015

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