One-dimensional stochastic Levy-Lorentz gas

We introduce a Levy-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 {xi(i)} are independent random variables identically distributed according to the probability density function mu(xi)similar to xi(-(1+gamma)). We show that under certain conditions the mean square displacement of the particle obeys < X-2(t)>greater than or equal to Ct(3-gamma) for I<gamma<2 This behavior is compatible with a renewal Levy walk scheme. We discuss the importance of ran events in the proper characterization of the diffusion process.