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.
Type de document :
Pré-publication, Document de travail
76 pages. 2010
Domaine :

https://hal.archives-ouvertes.fr/hal-00447444
Contributeur : Julien Berestycki <>
Soumis le : vendredi 15 janvier 2010 - 09:02:46
Dernière modification le : mercredi 12 octobre 2016 - 01:03:00

Identifiants

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

Citation

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

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