2025/12/26 by Dihang Guan, Hui He, Guan, Dihang +4
Economics, Econometrics and Finance · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · doi:10.48550/arxiv.2512.21906
openalex publication_date 2025/12/26 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28
We consider the wave propagation for a reaction-diffusion equation on the real line, with a random drift and Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) type nonlinear reaction. We show that when the average drift is positive, the asymptotic wave fronts propagating to the positive and negative directions are both pushed in the negative direction, leading to the possibility that both wave fronts propagate toward negative infinity. Our proof is based on the Large Deviations Principle for diffusion processes in random environments, as well as an analysis of the Feynman-Kac formula. Such probabilistic arguments also reveal the underlying physical mechanism of the wave fronts formation: the drift acts as an external field that shifts the (quenched) free-energy reference level without altering the intrinsic fluctuation structure of the system.