LEVY FLIGHTS IN RANDOM-ENVIRONMENTS

We consider Levy flights characterized by the step index fin a quenche d isotropic short-range random force field to one loop order. By means of a dynamic renormalization group analysis, we find that the dynamic exponent z for f < 2 locks onto f, independent of dimension and indep endent of the presence of weak quenched disorder. The critical dimensi on for f < 2 is given by d(c) = 2f - 2. For d < d(c) the disorder is r elevant, corresponding to a nontrivial fixed point for the force corre lation function. We also discuss the behavior of the subleading diffus ive term.