# Critical branching Brownian motion with absorption: survival probability

Abstract : We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of $-\sqrt{2}$. Kesten (1978) showed that almost surely this process eventually dies out. Here we obtain upper and lower bounds on the probability that the process survives until some large time $t$. These bounds improve upon results of Kesten (1978), and partially confirm nonrigorous predictions of Derrida and Simon (2007).
Keywords :
Type de document :
Pré-publication, Document de travail
2012
Domaine :

https://hal.archives-ouvertes.fr/hal-00766307
Contributeur : Julien Berestycki <>
Soumis le : mardi 18 décembre 2012 - 10:07:37
Dernière modification le : mardi 11 octobre 2016 - 14:10:32

### Identifiants

• HAL Id : hal-00766307, version 1
• ARXIV : 1212.3821

### Citation

Julien Berestycki, Nathanael Berestycki, Jason Schweinsberg. Critical branching Brownian motion with absorption: survival probability. 2012. <hal-00766307>

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