Title: Stochastic Homogenization for Reaction-Diffusion Equations

Abstract: We study heterogeneous reaction-diffusion equations in stationary ergodic random media with both ignition and KPP-type nonlinearities. Under suitable hypotheses on the environment, we prove the existence of deterministic asymptotic speeds of propagation for solutions with both compactly supported and front-like initial data. We subsequently obtain a general stochastic homogenization result which shows that, in the large-scale-large-time limit, the behavior of typical solutions in such environments is governed by a simple deterministic Hamilton-Jacobi equation modeling front propagation. This talk is based on joint work with Andrej Zlatos.