A Quenched Functional Central Limit Theorem for Random Walks in Random Environments under (T)_γ

2014/09/19 by Bouchet, Elodie, Sabot, Christophe, Santos, Renato Soares Dos · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1409.5528

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 [10] and Berger and Zeitouni in [2] 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 \Bbb E(τ²(ln τ)^1+m)1+1/γ, which allows the inclusion of new non-uniformly elliptic examples such as Dirichlet random environments.

Cited by

• Quenched scaling limit for biased random walks on random, heavy tailed conductances: low dimensions

Related

• The quenched central limit theorem for a model of random walk in random environment
• A local limit theorem for random walks in balanced environments
• Quenched local central limit theorem for random walks in a time-dependent balanced random environment
• Quenched Limits for Transient, Ballistic, Sub-Gaussian One-Dimensional Random Walk in Random Environment
• Quenched invariance principle for random walk in time-dependent balanced\n random environment