### The ∞-parent SLFV: Definition and growth properties

Probability Seminar

24th February 2023, 3:30 pm – 4:30 pm

Fry Building, 2.04

The ∞-parent spatial Lambda-Fleming Viot process, or ∞-parent SLFV, is a measure-valued population genetics process for expanding populations in a spatial continuum whose dynamics is reminiscent of the Eden growth model. As for other SLFV processes, its main feature is that the reproduction dynamics can be seen as "event-based" rather than "individual-based": the process is associated to a Poisson point process which indicates in which areas reproduction occurs at each instant. In this talk, I will first introduce three possible definitions of the process, each valid under more or less restrictive conditions on the underlying Poisson point process. I will then present what is currently known of the growth properties of the process: speed of growth of the front, of the bulk, and scaling of front fluctuations. The proof relies on a (self) duality relation satisfied by the process.

Based on a joint work with Amandine Véber (MAP5, Univ. Paris Cité) and an ongoing work with Matt Roberts (Univ. Bath) and Jan Lukas Igelbrink (GU Frankfurt and JGU Mainz).

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