Continuous-time random walks and traveling fronts

2002/09/18 by Sergei Fedotov, Vicenç Méndez · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum chaos and dynamical systems #stochastic dynamics and bifurcation

paper · pdf · doi:10.1103/physreve.66.030102

openalex publication_date 2002/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We present a geometric approach to the problem of propagating fronts into an unstable state, valid for an arbitrary continuous-time random walk with a Fisher-Kolmogorov-Petrovski-Piskunov growth/reaction rate. We derive an integral Hamilton-Jacobi type equation for the action functional determining the position of reaction front and its speed. Our method does not rely on the explicit derivation of a differential equation for the density of particles. In particular, we obtain an explicit formula for the propagation speed for the case of anomalous transport involving non-Markovian random processes.

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