The extremal process of two - speed branching Brownian motion ∗ Anton
نویسندگان
چکیده
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 σ1 for s ≤ bt and σ2 when bt ≤ s ≤ t. In the case σ1 > σ2, the process is the concatenation of two BBM extremal processes, as expected. In the case σ1 < σ2, 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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