## Fleming-Viot selects the minimal quasi-stationary distribution: the Galton-Watson case.(English. French summary)Zbl 1342.60145

Summary: Consider $$N$$ particles moving independently, each one according to a subcritical continuous-time Galton-Watson process unless it hits $$0$$, at which time it jumps instantaneously to the position of one of the other particles chosen uniformly at random. The resulting dynamics is called Fleming-Viot process. We show that for each $$N$$ there exists a unique invariant measure for the Fleming-Viot process, and that its stationary empirical distribution converges, as $$N$$ goes to infinity, to the minimal quasi-stationary distribution of the Galton-Watson process conditioned on non-extinction.

### MSC:

 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J25 Continuous-time Markov processes on general state spaces
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### References:

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