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) $\nu_c$. 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, $\nu_0$, as $N \to \infty$. Furthermore, every other qsd of the random walk ($\nu_c$, $c>0$) corresponds to a metastable state of the FV particle system.