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Uniform convergence of the Fleming-Viot process in a hard killing metastable case
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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.
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On uniform in time propagation of chaos in metastable cases: the Curie-Weiss model
For the Curie-Weiss model at β>1, the magnetization conditioned on staying positive converges uniformly in time to the positive mean-field steady-state trajectory, with polynomial-in-n error.
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