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 Lévy glass) have found that the transmission probability $T\propto 1/L^{\gamma }$ scales superdiffusively ($\gamma <1$). The data has been interpreted in terms of a Lévy walk. We present computer simulations to demonstrate that diffusive scaling ($\gamma \approx 1$) can coexist with a divergent second moment of the step size distribution [$p\left(s\right)\propto 1/s^{1+\alpha }$ 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 Lévy walk of independent steps.

• Received 20 May 2011

DOI:https://doi.org/10.1103/PhysRevE.85.021138