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 $\mathit{t}\mapsto \mathit{N}\mathit{t}$, this genetic information converges to the (very different) Fleming–Viot process from population genetics, as $\mathit{N}\to \infty$. An extension is provided to dynamics given by Brownian motion with hard catalyst killing at the boundary of its domain.