Diffusion with constant speed in a model phase space

Abstract

We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher-dimensional stochastic media (d > 1) where the particle can move along 2^d directions. We derive the equations for probability density function using the "formulae of differentiation" of Shapiro and Loginov. The model is an advancement over similiar models of photon migration in multiply scattering media for it results in a true diffusion at constant speed in the limit of large dimensions.