Electronic Journal of Probability

Tagged Particle Limit for a Fleming-Viot Type System

Ilie Grigorescu and Min Kang

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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.

Article information

Electron. J. Probab., Volume 11 (2006), paper no. 12, 311-331.

Accepted: 20 April 2006
First available in Project Euclid: 31 May 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J50: Boundary theory 35K15: Initial value problems for second-order parabolic equations

Fleming-Viot propagation of chaos tagged particle

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Grigorescu, Ilie; Kang, Min. Tagged Particle Limit for a Fleming-Viot Type System. Electron. J. Probab. 11 (2006), paper no. 12, 311--331. doi:10.1214/EJP.v11-316. https://projecteuclid.org/euclid.ejp/1464730547

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