# Critical branching Brownian motion with absorption: particle configurations

Abstract : 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.
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Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00766309
Contributor : Julien Berestycki <>
Submitted on : Tuesday, December 18, 2012 - 10:09:30 AM
Last modification on : Sunday, March 31, 2019 - 1:14:58 AM

### Identifiers

• HAL Id : hal-00766309, version 1
• ARXIV : 1212.3824

### Citation

Julien Berestycki, Nathanael Berestycki, Jason Schweinsberg. Critical branching Brownian motion with absorption: particle configurations. 2012. ⟨hal-00766309⟩

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