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