Scaling limit of the Fleming-Viot multicolor process
From MaRDI portal
Publication:6183254
DOI10.1214/23-AOP1654arXiv2110.05049OpenAlexW4388617933MaRDI QIDQ6183254
Author name not available (Why is that?)
Publication date: 26 January 2024
Published in: (Search for Journal in Brave)
Abstract: The Fleming-Viot process associated to a killed normally reflected diffusion is known to provide a particle representation for the quasi-stationary distribution of . In this paper we establish three results for this particle system. We firstly establish that it also provides a particle representation for the principal right eigenfunction of the submarkovian infinitesimal generator of . Secondly we establish that the Fleming-Viot process provides a representation for the -process. Thirdly we prove a conjecture due to Bieniek and Burdzy on the asymptotic distribution of the spine of the Fleming-Viot process and its side branches. We obtain these as corollaries of the following result. The Fleming-Viot multi-colour process is obtained by attaching genetic information to the particles in the Fleming-Viot process. We establish that under a suitable rescaling it converges to the Fleming-Viot superprocess from population genetics, with spatial inhomogeneity having the effect of speeding up the rate of genetic drift according to a simple formula.
Full work available at URL: https://arxiv.org/abs/2110.05049
No records found.
No records found.
This page was built for publication: Scaling limit of the Fleming-Viot multicolor process
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6183254)
