Transmission probability through a Levy glass and comparison with a Levy walk

Recent experiments on the propagation of light over a distance L through a random packing of spheres with a power-law distribution of radii (a so-called Levy glass) have found that the transmission probability T proportional to 1/L-gamma scales superdiffusively (gamma < 1). The data has been interpreted in terms of a Levy walk. We present computer simulations to demonstrate that diffusive scaling (gamma approximate to 1) can coexist with a divergent second moment of the step size distribution [p(s) proportional to 1/s(1+alpha) with alpha < 2]. This finding is in accord with analytical predictions for the effect of step size correlations, but deviates from what one would expect for a Levy walk of independent steps.