Mathieu Jonckere (Univ. Buenos Aires): Approximating quasi-stationary distributions with particles systems

Philosophers often argue that nothing lasts forever. In many mathematical models, processes too eventually vanish or get absorbed. However their long-time behaviour conditioned on non-absorption is well described by quasi-stationary distributions (QSDs). We study different particle systems like branching processes or Fleming Viot processes and show that under appropriate assumptions, their empirical measures converge to a target QSD. While the case of R-positive processes is fairly well understood, some results can be obtained for much more general cases. In particular, we partially address a conjecture of Kesten on the branching Brownian motion with drift killed in 0.