SCALING LIMIT OF THE FLEMING-VIOT MULTICOLOR PROCESS

Abstract

We consider the N-particle Fleming-Viot process associated to a normally reflected diffusion with soft catalyst killing. The Fleming-Viot multicolor process is obtained by attaching genetic information to the particles in the Fleming-Viot process. We establish that, after rescaling time by t _→ Nt, this genetic information converges to the (very different) Fleming-Viot process from population genetics, as N →∞. An extension is provided to dynamics given by Brownian motion with hard catalyst killing at the boundary of its domain.