Fleming-Viot particle system driven by a random walk on $\mathbb{N}$

Random walk on $\mathbb{N}$ with negative drift and absorption at 0, when conditioned on survival, has uncountably many invariant measures (quasi-stationary distributions, qsd) $ν_c$. We study a Fleming-Viot(FV) particle system driven by this process and show that mean normalized densities of the FV unique stationary measure converge to the minimal qsd, $ν_0$, as $N \to \infty$. Furthermore, every other qsd of the random walk ($ν_c$, $c>0$) corresponds to a metastable state of the FV particle system.

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