Abstract: for (transient) one dimensional random walk in random environment, conditions are known that ensure an annealed CLT. One then also have a quenched CLT, with a different (environment dependent) centering.
In higher dimensions, annealed CLT's have been derived in the ballistic case by Sznitman. We prove that in dimension 4 or more, annealed CLT's together with a mild integrability condition imply a quenched CLT. The proof is based on controlling the intersections of two RWRE paths in the same environment.
(joint work with N. Berger)