 
October 1, 2009: Jason
Schweinsberg (University of California, San Diego)
Title: The genealogy of branching Brownian motion with absorption.
Abstract: We consider a system of particles which
perform branching Brownian motion with negative drift and are killed upon
reaching zero, in the nearcritical regime where the total population stays
roughly constant with approximately N particles. We show that the
characteristic time scale for the evolution of this population is of order (log
N)^{3}, in the sense that when time is measured in these units, the
scaled number of particles converges to a version of Neveu's continuousstate
branching process. Furthermore, the genealogy of the particles is then governed
by a coalescent process known as the BolthausenSznitman coalescent. This
validates the nonrigorous predictions by Brunet, Derrida, Muller, and Munier
for a closely related model. This is joint work with Julien Berestycki and
Nathanael Berestycki.
