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Posted February 28, 2026

Probability Seminar Questions or comments?

Leo Tyrpak, University of Oxford
Fluctuations of spatial population models with non-local interactions

We analyse a class of spatial population models where the branching rate of particles depends non-locally on the whole empirical measure of particles. Scaling limits of this model have previously been shown to include the non-local Fisher-KPP equation and the porous medium equation. In this talk we will discuss the fluctuations of the process around these deterministic limits. We will show how an understanding of these can be applied to quantify the impact on geographical distance on genetic distance in the spirit of the classical Wright-Malecot formula.