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, 〈x²(t)〉, is linear in time (i.e., diffusive) for dimensions d2. In two dimensions, universal t/lnt corrections are found and for d=2-ε, the behavior is subdiffusive with 〈x²(t)〉~t^1-ε².