### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 311-331 |

Number of pages | 21 |

Journal | Electronic Journal of Probability |

Volume | 11 |

State | Published - 2006 |

### Fingerprint

### Keywords

- Absorbing brownian motio
- Fleming-viot
- Propagation of chaos
- Tagged particle

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Electronic Journal of Probability*,

*11*, 311-331.

**Tagged particle limit for a Fleming-Viot type system.** / Grigorescu, Ilie; Kang, Min.

Research output: Contribution to journal › Article

*Electronic Journal of Probability*, vol. 11, pp. 311-331.

}

TY - JOUR

T1 - Tagged particle limit for a Fleming-Viot type system

AU - Grigorescu, Ilie

AU - Kang, Min

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Absorbing brownian motio

KW - Fleming-viot

KW - Propagation of chaos

KW - Tagged particle

UR - http://www.scopus.com/inward/record.url?scp=33646401810&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646401810&partnerID=8YFLogxK

M3 - Article

VL - 11

SP - 311

EP - 331

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

SN - 1083-6489

ER -