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

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 under the assumption of large finite moments for the regeneration times. In this paper, we relax these moment assumptions under Sznitman's (T)γ ballisticity condition, which allows the inclusion of new non-uniformly elliptic examples such as Dirichlet random environments