One-dimensional stochastic Lévy-Lorentz gas

We introduce a Lévy-Lorentz gas in which a light particle is scattered by static point scatterers arranged on a line. We investigate the case where the intervals between scatterers [Formula Presented] are independent random variables identically distributed according to the probability density function [Formula Presented] We show that under certain conditions the mean square displacement of the particle obeys [Formula Presented] for [Formula Presented] This behavior is compatible with a renewal Lévy walk scheme. We discuss the importance of rare events in the proper characterization of the diffusion process.