Event
Pascal Maillard, Universit茅 Paris-Sud
Monday, February 26, 2018 14:00to15:00
Burnside Hall
Room 1214, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA
Branching Brownian motion with absorption at critical and near-critical drift.
Branching Brownian motion is a system of particles where particles branch at constant rate into two particles (say) and diffuse according to standard Brownian motions (there is no interaction between the particles apart from the branching). This process, and its discrete version, the branching random walk, have applications in many fields, including population models, reaction-diffusion equations, spin glasses and preferential attachment graphs. A natural extension of the model is to kill particles when they reach a certain point and to add a drift towards that point. There is a minimal drift at which the system dies out almost surely. In recent years, spectacular results have been obtained in the cases where the drift is at or just below this critical point. I will first review these results, then present work in progress on the critical case (joint work with Julien Berestycki and Jason Schweinsberg). Finally, I shall present work in progress (with Michel Pain) on the fluctuations of the Gibbs measure of branching Brownian motion (without absorption) at the critical temperature. Our methods are partly inspired by the recent work on branching Brownian motion with absorption.