Selection principle for the N-BBM and free boundary problems

par Julien Berestycki (Oxford University)

jeudi 26 mars 2026, 10:00 → 11:00 Europe/Paris

Salle K. Johnson

The N-BBM is an example of particle system with branching and selection. A fixed number of N particles move like Brownian motions, branch at rate 1 and, crucially, the leftmost particle is killed at each branching event, thus keeping the population size constant.
It is easy to see that, seen from the leftmost particle, this system has a unique invariant measure \pi_N. It has been conjectured for some time that, as N becomes large, \pi_N converges towards the minimal traveling wave solution to an associated free boundary problem. I will present a proof of this result (and other results concerning solutions of the free boundary problem) from a joint work with Sarah Penington and Oliver Tough.