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# Extreme values of spatial branching processes

Abstract : In this thesis, we are interested in extreme values of certain spatial branching processes such as the branching random walk and the branching Brownian motion. The branching random walk is a particle system that can be described as follows. It starts with an unique particle at generation $0$. It gives birth to a random number of children positioned with respect to their parent according to a point process. Then, each child repeats the same process to that of his parent and independently of the rest of particles. The branching Brownian motion can be described similarly. It starts with an unique particle at the origin. It moves according to a standard Brownian motion. After an exponential time, it dies giving birth to two children on its current position. Then, each child starts an independent branching Brownian motion. In the first part of this thesis, we study a model that interpolates between the branching random walk and a model linked to statistical physics which called \textit{Random energy model (REM)}. The next part of this thesis is devoted to the study of the extreme values of certain multitype branching processes. More precisely, we study the asymptotic behaviour of the extremal process of a reducible branching Brownian motion.
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https://tel.archives-ouvertes.fr/tel-03494699
Contributor : Mohamed Ali Belloum Connect in order to contact the contributor
Submitted on : Sunday, December 19, 2021 - 11:42:31 PM
Last modification on : Tuesday, January 4, 2022 - 5:47:22 AM
Long-term archiving on: : Sunday, March 20, 2022 - 6:53:13 PM

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• HAL Id : tel-03494699, version 1

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Mohamed Ali Belloum. Extreme values of spatial branching processes. Mathematics [math]. Université Sorbonne Naris Nord, 2021. English. ⟨tel-03494699⟩

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