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2014 The extremal process of two-speed branching Brownian motion
Anton Bovier, Lisa Hartung
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Electron. J. Probab. 19: 1-28 (2014). DOI: 10.1214/EJP.v19-2982


We construct and describe the extremal process for variable speed branching Brownian motion, studied recently by Fang and Zeitouni, for the case of piecewise constant speeds; in fact for simplicity we concentrate on the case when the speed is $\sigma_1$ for $s\leq bt$ and $\sigma_2$ when $bt\leq s\leq t$. In the case $\sigma_1>\sigma_2$, the process is the concatenation of two BBM extremal processes, as expected. In the case $\sigma_1<\sigma_2$, a new family of cluster point processes arises, that are similar, but distinctively different from the BBM process. Our proofs follow the strategy of Arguin, Bovier, and Kistler.


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Anton Bovier. Lisa Hartung. "The extremal process of two-speed branching Brownian motion." Electron. J. Probab. 19 1 - 28, 2014.


Accepted: 3 February 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1288.60108
MathSciNet: MR3164771
Digital Object Identifier: 10.1214/EJP.v19-2982

Primary: 60J80
Secondary: 60G70 , 82B44

Keywords: Branching Brownian motion , cluster point processes , extremal processes , Extreme values , F-KPP equation

Vol.19 • 2014
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