Non-Gaussian random walks

Abstract

The authors present an explicit expression for the probability distribution for the position of a continuous-time random walker in an arbitrary number of dimensions when the interjump density has a long time tail, in contrast to earlier results which require numerical inversion of a Fourier integral. They replace this numerical procedure by one that relies on the method of steepest descents. Their results are applied to diffusion on a comb and on a percolation cluster generated on a Cayley tree at criticality and are confirmed numerically.