  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 socalled
L\'evy 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 L\'evy 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(s) \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 L\'evy walk of independent steps.
