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

A persistent random walk can be regarded as a multidimensional Markov process. The bias-free telegraphers equation is partial derivative(2)p/partial derivativet(2) + 1/T partial derivativep/partial derivativet = v(2)del(2)p. It can be regarded as interpolating between the wave equation (T --> infinity) 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. (C) 2002 Elsevier Science B.V. All rights reserved.