  The recent realization of a "Levy glass" (a three-dimensional optical
material with a Levy distribution of scattering lengths) has motivated us to
analyze its one-dimensional analogue: A linear chain of barriers with
independent spacings s that are Levy distributed: p(s)~1/s^(1+alpha) for s to
infinity. The average spacing diverges for 0<alpha<1. A random walk along such
a sparse chain is not a Levy walk because of the strong correlations of
subsequent step sizes. We calculate all moments of conductance (or
transmission), in the regime of incoherent sequential tunneling through the
barriers. The average transmission from one barrier to a point at a distance L
scales as L^(-alpha) ln L for 0<alpha<1. The corresponding electronic shot
noise has a Fano factor (average noise power / average conductance) that
approaches 1/3 very slowly, with 1/ln L corrections.

Disordered Systems and Neural Networks