Persistent random walk
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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 (2\tau^{-1} \partial_t + \partial_{tt} - c_0^2 \partial_{xx}) n = 0 which is the telegrapher's equation.
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 (2\tau^{-1} \partial_t + \partial_{tt} - c_0^2 \partial_{xx}) n = 0 which is the telegrapher's equation.
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