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<NU>∂2p</NU>/∂t2</fr>+<fr style="s" shape="built" ALIGN="C"><NU>1</NU>/T</fr><hsp sp="0.16"><fr style="s" shape="built" ALIGN="C"><NU>∂p</NU>/∂t+<NU>1</NU>/T</fr><hsp sp="0.16"><fr style="s" shape="built" ALIGN="C"><NU>∂p</NU>/∂t <NU>∂p</NU>/∂t=v2∇2p .It can be regarded as interpolating between the wave equation <f>(T→∞)</f> and the diffusion equation <f>(T→0)</f>. 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. [Copyright &y& Elsevier]