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Tagged particle limit for a Fleming-Viot type system. (English) Zbl 1109.60083
Summary: We consider a branching system of $$N$$ Brownian particles evolving independently in a domain $$D$$ during any time interval between boundary hits. As soon as one particle reaches the boundary it is killed and one of the other particles splits into two independent particles, the complement of the set $$D$$ acting as a catalyst or hard obstacle. Identifying the newly born particle with the one killed upon contact with the catalyst, we determine the exact law of the tagged particle as $$N$$ approaches infinity. In addition, we show that any finite number of labelled particles become independent in the limit. Both results can be seen as scaling limits of a genome population undergoing redistribution present in the Fleming-Viot dynamics.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 35K15 Initial value problems for second-order parabolic equations 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
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