Branching Brownian motion and the road-field model

Stochastics Seminar
Thursday, April 18, 2024 - 3:30pm for 1 hour (actually 50 minutes)
Skiles 006
Nick Cook – Duke University – nickcook@math.duke.edu
Galyna Livshyts

The Fisher-KPP equation was introduced in 1937 to model the spread of an advantageous gene through a spatially distributed population. Remarkably precise information on the traveling front has been obtained via a connection with branching Brownian motion, beginning with works of McKean and Bramson in the 70s. I will discuss an extension of this probabilistic approach to the Road-Field Model: a reaction-diffusion PDE system introduced by H. Berestycki et al. to describe enhancement of biological invasions by a line of fast diffusion, such as a river or a road. Based on joint work with Amir Dembo.