Critical branching Brownian motion with absorption: particle configurations

We consider critical branching Brownian motion with absorption, in which there is initially a single particle at $x > 0$, particles move according to independent one-dimensional Brownian motions with the critical drift of $-\sqrt{2}$, and particles are absorbed when they reach zero. Here we obtain asymptotic results concerning the behavior of the process before the extinction time, as the position $x$ of the initial particle tends to infinity. We estimate the number of particles in the system at a given time and the position of the right-most particle. We also obtain asymptotic results for the configuration of particles at a typical time.

Data and Resources

Additional Info

Field Value
Source https://hal.science/hal-00766309
Author Berestycki, Julien, Berestycki, Nathanael, Schweinsberg, Jason
Maintainer CCSD
Last Updated May 30, 2026, 14:06 (UTC)
Created May 30, 2026, 14:06 (UTC)
Identifier hal-00766309
Language en
contributor Laboratoire de Probabilités et Modèles Aléatoires (LPMA) ; Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
creator Berestycki, Julien
date 2012-12-16T00:00:00
harvest_object_id d2dabcf1-7598-4d3d-a652-ecdb77dc01b0
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2025-12-29T00:00:00
relation info:eu-repo/semantics/altIdentifier/arxiv/1212.3824
set_spec type:UNDEFINED