From the Pain in the Torus to a Repulsion-Diffusion Equation
The phenomenon that underlies what Felsenstein famously dubbed “the pain in the torus” in 1975 can loosely be described as follows: In one and two dimensions, spatial population models with independent critical branching, and diffusive spatial motion, concentrate in increasingly few well-separated clumps, until they eventually die out. We illustrate this phenomenon with simulations, and sketch a proof in the setting of superBrownian motion.
Real populations do not behave in this way, and one of the reasons is that individuals migrate away from overcrowded areas. This effect can be incorporated into superBrownian motion as a pairwise repulsion between individuals. We explain how this relates to a certain (deterministic) repulsion-diffusion equation, for which we show well-posedness and give conditions on the strength of the repulsion that ensure global boundedness of solutions.
Date: 3 May 2023, 11:00 (Wednesday, 2nd week, Trinity 2023)
Venue: Mathematical Institute, Woodstock Road OX2 6GG
Venue Details: L3
Speaker: Peter Koepernik (University of Oxford)
Organising department: Department of Statistics
Organisers: Matthias Winkel (Department of Statistics, University of Oxford), Julien Berestycki (University of Oxford), Christina Goldschmidt (Department of Statistics, University of Oxford), James Martin (Department of Statistics, University of Oxford)
Part of: Probability seminar
Booking required?: Not required
Audience: Public
Editor: Christina Goldschmidt