Brownian bees in the infinite swarm limit
Date
Tuesday, January 7, 2020 16:30 - 17:30
Speaker
Julien Berestycki (University of Oxford)
Location
Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas
Contact
The "Brownian bees" model is a particle system in $\R^d$ in which particles move independently as Brownian motions, branch at rate one and the total population size is kept constant equal to N by removing the particle with maximum distance to the origin at each branching event. This type of spatial branching process with selection and its variants (such as the N-BBM) are simple models for the evolution of populations under selection. In this talk, I'll show how the large scale behaviour of these systems is given by the solutions of certain Free-boundary problems and how this can (or can't) be used to understand their large time behaviour.This is based on joint works in progress with E. Brunet, J. Nolen and S. Penington.