We prove a quenched central limit theorem for balanced random
walks in time dependent ergodic random environments. We assume that the environment satisfies appropriate ergodicity and ellipticity conditions. The proof is based on the use of a maximum principle for parabolic difference operators. We also discuss some non-elliptic environments and the related Harnack inequality.
(joint work with N. Berger, X.Guo and A. Ramirez)