Turbulence Without Pressure: Existence of the Invariant Measure

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.