## Electronic Journal of Probability

### The extremal process of two-speed branching Brownian motion

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 18, 28 pp.

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

https://projecteuclid.org/euclid.ejp/1465065660

Digital Object Identifier
doi:10.1214/EJP.v19-2982

Mathematical Reviews number (MathSciNet)
MR3164771

Zentralblatt MATH identifier
1288.60108

Rights

#### Citation

Bovier, Anton; Hartung, Lisa. The extremal process of two-speed branching Brownian motion. Electron. J. Probab. 19 (2014), paper no. 18, 28 pp. doi:10.1214/EJP.v19-2982. https://projecteuclid.org/euclid.ejp/1465065660

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