Ergodicity & travelling waves in a stochastic reaction-diffusion equation

In this talk, we survey some classical results on the speed of travelling waves in the FKPP equation, which is a stochastic reaction-diffusion equation arising in population genetics.

We review techniques used to prove the existence of a deterministic asymptotic wave speed in the FKPP equation. We focus in particular on the arguments used by Mueller & Sowers (1995) and Conlon & Doering (2005).

Time permitting, we will discuss the difficulties associated with generalizing results obtained for this model to travelling wave solutions in other SPDE.