Random walks in random environments.

A renormalization group analysis is carried out of the long time behavior of random walks in an environment with a positionally random local drift force. It is argued that, independent of the strength of the disorder, the mean square displacement, is linear in time, (i.e., diffusive), for dimensions d>~2. In two dimensions, universal t/lnt corrections are found and in d=2-e, the behavior is sub-diffusive with ~t (1-e)(2).