### Generalized Fleming-Viot Processes with Mutations

Mytnik, L *(Technion)*

Thursday 13 September 2012, 09:00-09:50

Seminar Room 1, Newton Institute

#### Abstract

We consider a generalized Fleming-Viot process with index $\alpha \in (1,2)$ with constant mutation rate $\theta>0$. We show that for any $\theta>0$, with probability one, there are no times at which there is a finite number of types in the population. This is different from the corresponding result of Schmuland for a classical Fleming-Viot process, where such times exist for $\theta$ sufficiently large. Along the proof we introduce a measure-valued branching process with non-Lipschitz interactive immigration which is of independent interest.

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