Uniform in time weak convergence for a Fleming-Viot particle system with hard killing
Abstract
This paper is concerned with the Fleming-Viot particle system introduced by Burdzy, Hołyst and March (2000). In this model, N Brownian particles evolve independently in a bounded domain D until one of the particles reaches the boundary. Then, the particle which has hit the boundary instantaneously jumps to the location of one of the other particles, chosen uniformly at random. Burdzy, Hołyst and March showed that when N tends to infinity, the empirical measure of the system converges to a solution to the heat equation on D with Dirichlet boundary conditions, renormalized to have total mass $1$. Our main result is a sharp, uniform-in-time, quantitative version of this result. We employ the method of weak propagation of chaos, which necessitates a careful study of the (backward) Kolmogorov equations associated to the N-particle systems, and the infinite-dimensional transport equation whose characteristics are given by renormalized solutions of the Dirichlet heat equation. The proofs are entirely analytical, and most of the technical effort is devoted to building barrier functions which are used to control the singular behavior of the system when most of the particles approach the boundary.
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BibTeX
@misc{cardaliaguet2026uniform,
title = {{Uniform in time weak convergence for a Fleming-Viot particle system with hard killing}},
author = {Pierre Cardaliaguet and Marco Cirant and Joe Jackson and Panagiotis E. Souganidis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22561},
eprint = {2609.22561},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22561},
}
RIS
TY - UNPB
TI - Uniform in time weak convergence for a Fleming-Viot particle system with hard killing
AU - Pierre Cardaliaguet
AU - Marco Cirant
AU - Joe Jackson
AU - Panagiotis E. Souganidis
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.22561
UR - https://arxiv.org/abs/2609.22561
AB - This paper is concerned with the Fleming-Viot particle system introduced by Burdzy, Hołyst and March (2000). In this model, N Brownian particles evolve independently in a bounded domain D until one of the particles reaches the boundary. Then, the particle which has hit the boundary instantaneously jumps to the location of one of the other particles, chosen uniformly at random. Burdzy, Hołyst and March showed that when N tends to infinity, the empirical measure of the system converges to a solution to the heat equation on D with Dirichlet boundary conditions, renormalized to have total mass $1$. Our main result is a sharp, uniform-in-time, quantitative version of this result. We employ the method of weak propagation of chaos, which necessitates a careful study of the (backward) Kolmogorov equations associated to the N-particle systems, and the infinite-dimensional transport equation whose characteristics are given by renormalized solutions of the Dirichlet heat equation. The proofs are entirely analytical, and most of the technical effort is devoted to building barrier functions which are used to control the singular behavior of the system when most of the particles approach the boundary.
ER -