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arXiv · 1308.1868

The extremal process of two-speed branching Brownian motion

Anton Bovier·Lisa Hartung
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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 $σ_1$ for $s\leq bt$ and $σ_2$ when $bt\leq s\leq t$. In the case $σ_1>σ_2$, the process is the concatenation of two BBM extremal processes, as expected. In the case $σ_1<σ_2$, 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. 2013-12-18. The extremal process of two-speed branching Brownian motion. https://arxiv.org/abs/1308.1868

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