Uniform convergence of the Fleming-Viot process in a hard killing metastable case

TL;DR

This paper proves that a Fleming-Viot process, modeling a metastable diffusion with killing, converges exponentially fast to a stationary measure uniformly over time, with results independent of system size.

Contribution

It establishes the exponential convergence and uniform propagation of chaos for the Fleming-Viot process in a metastable setting, using a coupling approach.

Findings

Exponential convergence to stationary measure.

Uniform in time propagation of chaos.

Convergence rate independent of system size.

Abstract

We study the long-time convergence of a Fleming-Viot process, in the case where the underlying process is a metastable diffusion killed when it reaches some level set. Through a coupling argument, we establish the long-time convergence of the Fleming-Viot process toward some stationary measure at an exponential rate independent of $N$, the size of the system, as well as uniform in time propagation of chaos estimates.