Scaling Limit of the Fleming-Viot Multi-Colour Process

Abstract

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