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 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 non-rigorous predictions by Brunet, Derrida, Muller, and Munier for a closely related model.
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https://hal.archives-ouvertes.fr/hal-00447444
Contributor : Julien Berestycki <>
Submitted on : Friday, January 15, 2010 - 9:02:46 AM
Last modification on : Wednesday, October 12, 2016 - 1:03:00 AM

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  • HAL Id : hal-00447444, version 1
  • ARXIV : 1001.2337

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Julien Berestycki, Nathanael Berestycki, Jason Schweinsberg. The genealogy of branching Brownian motion with absorption. 76 pages. 2010. <hal-00447444>

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