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We show, for a class of discrete Fleming-Viot (or Moran) type particlesystems, that the convergence to the equilibrium is exponential for a suitableWassertein coupling distance. The approach provides an explicit quantitativeestimate on the rate of convergence. As a consequence, we show that theconditioned process converges exponentially fast to a unique quasi-stationarydistribution. Moreover, by estimating the two-particle correlations, we provethat the Fleming-Viot process converges, uniformly in time, to the conditionedprocess with an explicit rate of convergence. We illustrate our results on theexamples of the complete graph and of N particles jumping on two points.

Quantitative results for the Fleming-Viot Particle system and quasi-stationary distributions in discrete space