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 $N \to \infty$\mathrm{.}Furthermore,everyotherqsdoftherandomwalk($\nu_c$,$c>0$) corresponds to a metastable state of the FV particle system.