A STOCHASTIC APPROACH TO ENHANCED DIFFUSION - LEVY WALKS

We study anomalous transport in one-dimension through L6vy walks and concentrate on the superlinear diffusion regime. The problem is formulated in terms of continuous-time random walks (CTRW) with kernels that couple space and time. We calculate P(r, t), the probability of being at position r at time t, and <r2(<)), the mean-squared displacement for which we present approximate asymptotic forms. We examine the relationship between L6vy walks and L6vy distributions and discuss the validity range of the asymptotic (heuristic) relation P(0, t)~ (r2(t))-V2. © 1990 IOP Publishing Ltd.