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arXiv · 1212.3821

Critical branching Brownian motion with absorption: survival probability

Julien Berestycki·Nathanael Berestycki·Jason Schweinsberg
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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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Julien Berestycki, Nathanael Berestycki, Jason Schweinsberg. 2012-12-18. Critical branching Brownian motion with absorption: survival probability. https://arxiv.org/abs/1212.3821

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