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

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  • Bouchet, Élodie
  • Sabot, Christophe
  • dos Santos, Renato Soares

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.

Suggested Citation

  • Bouchet, Élodie & Sabot, Christophe & dos Santos, Renato Soares, 2016. "A quenched functional central limit theorem for random walks in random environments under (T)γ," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1206-1225.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:4:p:1206-1225
    DOI: 10.1016/j.spa.2015.10.015
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    Cited by:

    1. Buraczewski, Dariusz & Dyszewski, Piotr & Iksanov, Alexander & Marynych, Alexander, 2020. "Random walks in a strongly sparse random environment," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 3990-4027.

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