Levy walks in quenched disordered media 

We study Levy walks in quenched random and detrministic
one-dimensional media, with scatterers spaced according to a
long-tailed distribution. By analyzing the scaling relations for the
random-walk probability, we obtain the asymptotic behavior of the mean
square displacement as a function of the exponent characterizing the
scatterers distribution. We demonstrate that different average
procedures can display different asymptotic behavior. In particular,
we estimate the moments of the displacement averaged over processes
starting from scattering sites. Our results are compared with
numerical simulations, with excellent agreement.