Local limit theorem and equivalence of dynamic and static points of view for certain ballistic random walks in i.i.d. environments

Noam Berger, Moran Cohen, Ron Rosenthal

Published 2014-05-27, updated 2016-09-02Version 2

In this work, we discuss certain ballistic random walks in random environments on $\mathbb{Z}^d$, and prove the equivalence between the static and dynamic points of view in dimension $d\geq4$. Using this equivalence, we also prove a version of a local limit theorem which relates the local behavior of the quenched and annealed measures of the random walk by a prefactor.