%0 Generic %1 berestycki2010bbm %A Berestycki, Julien %A Berestycki, Nathanael %A Schweinsberg, Jason %D 2010 %K bolthausen-sznitman_coalescent continuous-state_branching_processes genealogies branching_Brownian_motion %T The genealogy of branching Brownian motion with absorption %U http://arxiv.org/abs/1001.2337 %X 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.

@misc{berestycki2010bbm, 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. }, added-at = {2010-09-03T18:10:51.000+0200}, author = {Berestycki, Julien and Berestycki, Nathanael and Schweinsberg, Jason}, biburl = {https://www.bibsonomy.org/bibtex/2127b51beac2b9c77b3af2cb7ec861ae6/peter.ralph}, description = {[1001.2337] The genealogy of branching Brownian motion with absorption}, interhash = {1fec1cadfbe9f020594c44246cb3caa0}, intrahash = {127b51beac2b9c77b3af2cb7ec861ae6}, keywords = {bolthausen-sznitman_coalescent continuous-state_branching_processes genealogies branching_Brownian_motion}, note = {cite arxiv:1001.2337 Comment: 76 pages}, timestamp = {2012-04-23T01:33:35.000+0200}, title = {The genealogy of branching Brownian motion with absorption}, url = {http://arxiv.org/abs/1001.2337}, year = 2010 }