# The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential

Abstract : In this note we consider a branching Brownian motion (BBM) on $\mathbb{R}$ in which a particle at spatial position $y$ splits into two at rate $\beta y^2$, where $\beta>0$ is a constant. This is a critical breeding rate for BBM in the sense that the expected population size blows up in finite time while the population size remains finite, almost surely, for all time. We find an asymptotic for the almost sure rate of growth of the population.
Type de document :
Pré-publication, Document de travail
2009
Domaine :
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00440212
Contributeur : Julien Berestycki <>
Soumis le : mercredi 9 décembre 2009 - 17:42:15
Dernière modification le : jeudi 11 janvier 2018 - 06:12:29

### Identifiants

• HAL Id : hal-00440212, version 1
• ARXIV : 0912.1360

### Citation

J. Berestycki, Eric Brunet, J. W. Harris, S. C. Harris. The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential. 2009. 〈hal-00440212〉

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