persistent random walk

{{Short description|Modification of the random walk model}}

The persistent random walk is a modification of the random walk model.

A population of particles are distributed on a line, with constant speed $c\_0$, and each particle's velocity may be reversed at any moment. The reversal time is exponentially distributed as $e^\{-t/\backslash tau\}/\backslash tau$, then the population density $n$ evolves according to{{Cite journal |last=Weiss |first=George H |date=2002-08-15 |title=Some applications of persistent random walks and the telegrapher's equation |url=https://www.sciencedirect.com/science/article/pii/S0378437102008051 |journal=Physica A: Statistical Mechanics and its Applications |volume=311 |issue=3 |pages=381–410 |doi=10.1016/S0378-4371(02)00805-1 |issn=0378-4371}}$$(2\backslash tau^\{-1\}\; \backslash partial\_t\; +\; \backslash partial\_\{tt\}\; -\; c\_0^2\; \backslash partial\_\{xx\})\; n\; =\; 0$$which is the telegrapher's equation.