Random Walks with Bivariate Levy-Stable Jumps in Comparison with Levy Flights

In this paper we compare the Levy flight model on a plane with the random walk resulting from bivariate Levy-stable random jumps with the uniform spectral measure. We show that, in general, both processes exhibit similar properties, i.e. they are characterized by the presence of the jumps with extremely large lengths and uniformly distributed directions (reflecting the same heavy-tail behavior and the spherical symmetry of the jump distributions), connecting characteristic clusters of short steps. The bivariate Levy-stable random walks, belonging to the class of the well investigated stable processes, can enlarge the class of random-walk models for transport phenomena if other than uniform spectral measures are considered. (author)