The extremal process of two-speed branching Brownian motion

@article{Bovier2013TheEP,
  title={The extremal process of two-speed branching Brownian motion},
  author={Anton Bovier and Lisa Hartung},
  journal={Electronic Journal of Probability},
  year={2013},
  volume={19},
  pages={1-28}
}
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… 
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