Local limit theorem and equivalence of dynamic and static points of view   for certain ballistic random walks in i.i.d. environments
  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. 
Noam Berger, Moran Cohen, Ron Rosenthal
math.PR