The extremal process of a cascading family of branching Brownian motion

Mohamed Ali Belloum

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arXiv · 2202.01584

The extremal process of a cascading family of branching Brownian motion

Mohamed Ali Belloum

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Abstract

We study the asymptotic behaviour of the extremal process of a cascading family of branching Brownian motions. This is a particle system on the real line such that each particle has a type in addition to his position. Particles of type $1$ move on the real line according to Brownian motions and branch at rate $1$ into two children of type $1$. Furthermore, at rate $\alpha$, they give birth to children too of type $2$. Particles of type $2$ move according to standard Brownian motion and branch at rate $1$, but cannot give birth to descendants of type $1$. We obtain the asymptotic behaviour of the extremal process of particles of type $2$.

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Mohamed Ali Belloum. 2022-02-03. The extremal process of a cascading family of branching Brownian motion. https://arxiv.org/abs/2202.01584

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