Some applications of persistent random walks and the telegrapher's equation

Abstract

A persistent random walk can be regarded as a multidimensional Markov process. The bias-free telegraphers equation is ∂ 2p ∂t 2 + 1 T ∂p ∂t =v 2 ∇ 2p . It can be regarded as interpolating between the wave equation ( T→∞) and the diffusion equation ( T→0). Previously, it has found application in thermodynamics (cf. the review in Rev. Mod. Phys. 61 (1989) 41; 62 (1990) 375). More recent applications are reviewed in the present article.