One-dimensional stochastic Levy-Lorentz gas

We introduce a Levy-Lorentz gas in which a light particle is scattered by s tatic point scatterers arranged on a line. We investigate the case where th e intervals between scatterers {xi(i)} are independent random variables ide ntically distributed according to the probability density function mu(xi)si milar to xi(-(1+gamma)). We show that under certain conditions the mean squ are 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 wal k scheme. We discuss the importance of ran events in the proper characteriz ation of the diffusion process.