# PS : Mohamed Ali Belloum (Univ. Paris Nord) : Asymptotic behaviour of the maximal displacement in the reducible multitype branching Brownian motion

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# PS : Mohamed Ali Belloum (Univ. Paris Nord) : Asymptotic behaviour of the maximal displacement in the reducible multitype branching Brownian motion

## 18 mai / 11:30 - 12:30

Branching Brownian motion is a particle system in the real line in which particles move according to independent standard Brownian motion and split into two offspring at constant rate $\beta$.

In this talk we take interest in a two type version of branching Brownian motion that can be described as follows.

Particles of type $1$ move according to Brownian motions with diffusion coefficient $\sigma^2_1$ and branch at rate $\beta_1$ into two children of type $1$. Additionally, they give birth to particles of type $2$ at rate $\alpha$.

Particles of type $2$ move according to Brownian motions with diffusion coefficient $\sigma^2_2$ and branch at rate $\beta_2$, but cannot give birth to descendants of type $1$, therefore, the type structure of this two type branching process is reducible.

We show the existence of three regions that the state space $(\beta,\sigma^2)$ belongs to. In each region we have a different behaviour of the extremal process.

In particular, we explored the case of the anomalous spreading that was introduced by Biggins (2012), where the speed of the right most particle in a multitype branching random walk is larger than the speed in a BBM consisting only one type of particles.

Exposé sur Zoom (lien sur demande)

PS : Mohamed Ali Belloum (Univ. Paris Nord) : Asymptotic behaviour of the maximal displacement in the reducible multitype branching Brownian motion

## Détails

Date :
18 mai
Heure :
11:30 - 12:30
Catégorie d’évènement:

Alexis Devulder
Julien Worms