Ray propagation in a random lattice: a maximum entropy, anomalous diffusion Process

Abstract

The typical model for diffusion in disordered systems is that of a random walk that proceeds in discrete steps over a random lattice, where not all the nearest sites can be reached at each step. We study the related problem of ray propagation in percolating lattices, and observe that it follows an anomalous diffusion process, whose appropriate metric is the "Manhattan" distance defined by the lattice geometry. The proposed solution is the one that exhibits the maximum Shannon's entropy, among all propagation processes with appropriate moment constraints imposed by the geometry of the lattice. Ray propagation in percolating lattices has been recently proposed as a model for urban area propagation of radio waves. We discuss implications of our results in this scenario.