MBAP-P : Markov Branching Additive Processes Project

Members

• Manon Costa, IMT, Université de Toulouse
• Thierry Klein, IMT, Université de Toulouse
• Agnès Lagnoux, IMT, Université de Toulouse
• Pascal Maillard, IMT, Université de Toulouse
• Bastien Mallein, IMT, Université de Toulouse
• Michel Pain, IMT, Université de Toulouse
• Pierre Petit, IMT, Université de Toulouse

Description of the project

Spatial branching process describe a class of particle systems in which individuals move independently of one another, according to some Markov process. In addition, the particles give birth at random to children, who then start independent copy of the same process. This type of processes can be used to model a large variety of phenomenon, from epidemics and natural selection to neutrons in a nuclear reactor. In addition, their study is directly linked, by a duality argument, to reaction diffusion equations. Spatial branching processes also appear in statistical physics as toy-models for the study of spin-glasses or the Liouville quantum gravity, and in high-energy physics to stydy electron-hardron interactions.
Natural classes of spatial branching processses include branching random walks, branching Brownian motions and branching Lévy processes. For these processes, the asymptotic behaviour of the position of their extrema is now well-known. The distribution of the extrema usually converge to a decorated Poisson point process with a random intensity.
The aim of this project is to extend this understanding to a larger class, in which the motion of particles is not a random walk or a Lévy process, but a Markov additive process. Some early results can be found in the literature (on-off branching Brownian motion, mutltitype branching random walk, etc.). Our objective is to find a natural class of processes encompassing all these examples, and to study their asymptotic properties, such as their extremal process.

Open position

A post-doctoral position, starting in the second half of 2025 is now open for candidacy. Applications should be send to me, with a letter of motivation and a scientific curriculum vitae, as well as the name of two people that can be contacted for a reference letter. More details can be found on the following job description.