Date: Tuesday, October 7, 2003
Time: 4:30 pm
Location: 117 Hayes-Healy Hall
(Refreshments at 4:00pm, in 257 Hurley Hall)

Speaker: Prof. Charles R. Doering

From: Department of Mathematics and Michigan Center for Theoretical Physics
University of Michigan, Ann Arbor, MI, USA

Title: "The Stochastic Fisher-Kolmogorov-Petrovsky-Piscunov Equation, Interacting Particles, and Duality"

Abstract:
The Fisher-Kolmogorov-Petrovsky-Piscunov (FKPP) equation is a classical model used to describe the evolution of a spatially distributed population with local logistic (growth-saturation) dynamics and diffusive spreading. It is a `mean-field' model in the sense that all discreteness and noise effects are neglected. In this talk we describe a rigorous connection between a stochastic FKPP partial differential equation with a particular form of multiplicative noise and a single species birth- coalescence reaction-diffusion particle system. The correspondence is not in terms of a fluctuating hydrodynamic description for the reaction-diffusion model, but rather via the concept of `duality', an idea that has played a major role in the probabilistic analysis of interacting particle systems in recent decades. The idea of duality will be discussed and used to derive an exact formula for the extinction probability of any initial configuration for the stochastic FKPP equation. Duality will also be used to exploit the connection between the diffusion-limited birth-coalescence process and the strong-noise limit of the stochastic FKPP equation to determine the effect of high noise levels on the propagation speed of a wavefront in this stochastic pde. This is joint work with Carl Mueller (University of Rochester) and Peter Smereka (University of Michigan)