Electronic Journal of Probability
- Electron. J. Probab.
- Volume 19 (2014), paper no. 18, 28 pp.
The extremal process of two-speed branching Brownian motion
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.
Electron. J. Probab., Volume 19 (2014), paper no. 18, 28 pp.
Accepted: 3 February 2014
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G70: Extreme value theory; extremal processes 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.)
This work is licensed under a Creative Commons Attribution 3.0 License.
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