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 $s\le bt$ and ${\sigma }_2$ when $bt\le s\le t$. 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.

28 pages; revised version

References in corpus (1)

• Slowdown for time inhomogeneous branching Brownian motion

Cited by in corpus (1)

• Freezing and decorated Poisson point processes