The Fleming Viot process driven by subcritical branching: a selection principle

Speaker : Matthieu Jonkheere
Date: 25/01/2012
Time: 2:00 pm - 3:00 pm
Location: LINCS Meeting Room 40


We consider Fleming Viot processes having the following dynamics: N particles move independently according to the dynamics of a subcritical branching process until they hit 0, at which point, they instantaneously and uniformly choose the position of one of the other particles. We first establish a coupling between the FV processes (associated to any one-dimensional dynamics) and multitype branching processes. This allows us to prove convergence of scaled version of the FV processes and ergodicity for fixed N. Using large deviations estimate for subcritical branching processes, this coupling further allows to obtain useful drift inequalities for the maximum of the Fleming Viot process. These inequalities imply in turn tightness of the family of empirical measures under measure of the branching process when N tends to infinity. the stationary measure of the FV process. Finally, we prove a selection principle: the empirical measures converge to the extremal quasi-stationary measure of the branching process when N tends to infinity.