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November 2023 Scaling limit of the Fleming–Viot MultiColor process
Oliver Tough
Author Affiliations +
Ann. Probab. 51(6): 2345-2386 (November 2023). DOI: 10.1214/23-AOP1654


We consider the N-particle Fleming–Viot process associated to a normally reflected diffusion with soft catalyst killing. The Fleming–Viot multicolor process is obtained by attaching genetic information to the particles in the Fleming–Viot process. We establish that, after rescaling time by tNt, this genetic information converges to the (very different) Fleming–Viot process from population genetics, as N. An extension is provided to dynamics given by Brownian motion with hard catalyst killing at the boundary of its domain.

Funding Statement

This work was partially funded by grant 200020 196999 from the Swiss National Foundation and by the EPSRC MathRad programme grant EP/W026899/.


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Oliver Tough. "Scaling limit of the Fleming–Viot MultiColor process." Ann. Probab. 51 (6) 2345 - 2386, November 2023.


Received: 1 January 2022; Revised: 1 July 2023; Published: November 2023
First available in Project Euclid: 12 November 2023

Digital Object Identifier: 10.1214/23-AOP1654

Primary: 60J80 , 60K35
Secondary: 92D15

Keywords: Fleming–Viot process (particle system) , Fleming–Viot process (population genetics)

Rights: This research was funded, in whole or in part, by [EPSEC/UKRI, EP/W026899]. A CC BY 4.0 license is applied to this article arising from this submission, in accordance with the grant's open access conditions.

Vol.51 • No. 6 • November 2023
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