# Anomalous spreading in reducible multitype branching Brownian motion

Abstract : We consider a two-type reducible branching Brownian motion, defined as a two type branching particle system on the real line, in which particles of type $1$ can give birth to particles of type $2$, but not reciprocally. This process has been shown by Biggins to exhibit an anomalous spreading behaviour under specific conditions: in that situation, the rightmost particle at type $t$ is much further than the expected position for the rightmost particle in a branching Brownian motion consisting only of particles of type $1$ or of type $2$. This anomalous spreading also has been investigated from a reaction-diffusion equation standpoint by Holzer. The aim of this article is to refine the previous results and study the asymptotic behaviour of the extremal process of the two-type reducible branching Brownian motion. If the branching Brownian motion exhibits an anomalous spreading behaviour, its asymptotic differs from what it typically expected in branching Brownian motions.
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Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-03048378
Contributor : Bastien Mallein <>
Submitted on : Wednesday, December 9, 2020 - 12:15:53 PM
Last modification on : Wednesday, December 16, 2020 - 3:36:26 AM

### File

bbmMultitype.pdf
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### Identifiers

• HAL Id : hal-03048378, version 1
• ARXIV : 2011.03223

### Citation

Mohamed Ali Belloum, Bastien Mallein. Anomalous spreading in reducible multitype branching Brownian motion. 2020. ⟨hal-03048378⟩

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