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2015 Maximal displacement in the $d$-dimensional branching Brownian motion
Bastien Mallein
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Electron. Commun. Probab. 20: 1-12 (2015). DOI: 10.1214/ECP.v20-4216


We consider a branching Brownian motion evolving in $\mathbb{R}^d$. We prove that the asymptotic behaviour of the maximal displacement is given by a first ballistic order, plus a logarithmic correction that increases with the dimension $d$. The proof is based on simple geometrical evidence. It leads to the interesting following side result: with high probability, for any $d \geq 2$, individuals on the frontier of the process are close parents if and only if they are geographically close.


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Bastien Mallein. "Maximal displacement in the $d$-dimensional branching Brownian motion." Electron. Commun. Probab. 20 1 - 12, 2015.


Accepted: 24 October 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60307
MathSciNet: MR3417448
Digital Object Identifier: 10.1214/ECP.v20-4216

Primary: 60J65
Secondary: 60J70 , 60J80

Keywords: Branching Brownian motion , branching process , Brownian motion

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