Persistent random walk explained

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/\tau} /\tau , then the population density n evolves according to^[1] $$(2\backslash tau^\; \backslash partial\_t\; +\; \backslash partial\_\; -\; c\_0^2\; \backslash partial\_)\; n\; =\; 0$$which is the telegrapher's equation.

Notes and References

1. Weiss . George H . 2002-08-15 . Some applications of persistent random walks and the telegrapher's equation . Physica A: Statistical Mechanics and its Applications . 311 . 3 . 381–410 . 10.1016/S0378-4371(02)00805-1 . 0378-4371.