##### Department of Mathematics,

University of California San Diego

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### Math 288 - Probability and Statistics Seminar

## Jason Schweinsberg

#### UCSD

## 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 near-critical 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 continuous-state branching process. Furthermore, the genealogy of the particles is then governed by a coalescent process known as the Bolthausen-Sznitman coalescent. This validates the non-rigorous predictions by Brunet, Derrida, Muller, and Munier for a closely related model. This is joint work with Julien Berestycki and Nathanael Berestycki.

### October 1, 2009

### 10:00 AM

### AP&M 6402

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