A branching Brownian motion perspective on the Road-Field Model

The Fisher-KPP equation was proposed in 1937 as a model for the spread of an advantageous gene through a one-dimensional habitat, such as a shoreline. Since then, remarkably precise information on the location of the traveling front has been achieved through a connection with branching Brownian motion, beginning with influential work of Bramson in 1978.

In this talk I will discuss an extension of this probabilistic approach to the Road-Field Model: a coupled PDE system introduced in recent work of Berestycki, Roquejoffre and Rossi for the enhancement of the propagation of an invasive species by a line of fast diffusion, such as a river or a road.

This is ongoing work with Amir Dembo.