On the Satic and Dynamic Points of View for Certain Random Walks in Random Environment

Abstract

In this work we prove the equivalence between static and dynamic points of views for certain ballistic random walks in random environment on Z^d, when d greater than or equal to 4 and the disorder is low. Our techniques also enable us to derive in the same setting a functional central limit theorem for almost every realization of the environment. We also provide an example where the equivalence between static and dynamic points of views breaks down.