Branching Brownian motion with selection and a free boundary problem

Consider a system of N particles moving according to Brownian motions and branching at rate one. Each time a particle branches, the particle in the system furthest from the origin is killed. It turns out that we can use results about a related partial differential equation known as a free boundary problem to control the long term behaviour of this particle system for large N.

This is joint work with Julien Berestycki, Eric Brunet and James Nolen.