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March 2013 The genealogy of branching Brownian motion with absorption
Julien Berestycki, Nathanaël Berestycki, Jason Schweinsberg
Ann. Probab. 41(2): 527-618 (March 2013). DOI: 10.1214/11-AOP728

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 variant 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 nonrigorous predictions by Brunet, Derrida, Muller and Munier for a closely related model.

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Julien Berestycki. Nathanaël Berestycki. Jason Schweinsberg. "The genealogy of branching Brownian motion with absorption." Ann. Probab. 41 (2) 527 - 618, March 2013. https://doi.org/10.1214/11-AOP728

Information

Published: March 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1304.60088
MathSciNet: MR3077519
Digital Object Identifier: 10.1214/11-AOP728

Subjects:
Primary: 60J99
Secondary: 60F17 , 60G15 , 60J80

Keywords: Bolthausen–Sznitman coalescent , Branching Brownian motion , continuous-state branching processes

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 2 • March 2013
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