Some applications of persistent random walks and the telegrapherʹs equation

A persistent random walk can be regarded as a multidimensional Markov process. The bias-free telegraphers equation is 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.