# 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).
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Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00766307
Contributor : Julien Berestycki <>
Submitted on : Tuesday, December 18, 2012 - 10:07:37 AM
Last modification on : Sunday, March 31, 2019 - 1:14:27 AM

### Identifiers

• 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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