Tagged Particle Limit for a Fleming-Viot Type System
Ilie A Grigorescu and Min Kang, University of Miami and North Carolina State University
Abstract
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.
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