A quenched functional central limit theorem for random walks in random environments under

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• 作者：É ; lodie Bouchet^a ; ^{bouchet@math.univ-lyon1.fr" class="auth_mail" title="E-mail the corresponding author} ; Christophe Sabot^a ; ^{sabot@math.univ-lyon1.fr" class="auth_mail" title="E-mail the corresponding author} ; Renato Soares dos Santos^b ; ^{soares@wias-berlin.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60F05 ; 60G52
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：126
• 期：4
• 页码：1206-1225
• 全文大小：283 K

文摘

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)_γiner hidden">${\left(T\right)}_{\gamma }$ condition of Sznitman we reduce the moment condition to E(τ²(lnτ)^1+m)<+&infin;iner hidden">$\mathbb{E}\left({\tau }^2{(ln\tau )}^{1+m}\right)<+\mathrm{\&<font\; color="red">in</font>f<font\; color="red">in</font>;}$ for m>1+1/γiner hidden">$m>1+1/\gamma$, which allows the inclusion of new non-uniformly elliptic examples such as Dirichlet random environments.