Quantitative results for the Fleming-Viot particle system in discrete space

We show, for a class of discrete Fleming-Viot type particle systems, that the convergence to the equilibrium is exponential for a suitable Wassertein coupling distance. The approach provides an explicit quantitative estimate on the rate of convergence. As a consequence, we show that the conditioned process converges exponentially fast to a unique quasi-stationary distribution. Moreover, by estimating the two-particle correlations, we prove that the Fleming-Viot process converges, uniformly in time, to the conditioned process with an explicit rate of convergence. We illustrate our results on the examples of the complete graph and of the two point space

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

We show, for a class of discrete Fleming-Viot (or Moran) type particle systems, that the convergence to the equilibrium is exponential for a suitable Wassertein coupling distance. The approach provides an explicit quantitative estimate on the rate of convergence. As a consequence, we show that the conditioned process converges exponentially fast to a unique quasi-stationary distribution. Moreover, by estimating the two-particle correlations, we prove that the Fleming-Viot process converges, uniformly in time, to the conditioned process with an explicit rate of convergence. We illustrate our results on the examples of the complete graph and of N particles jumping on two points.Comment: New version of the paper "Quantitative results for the Fleming-Viot particle system in discrete space ". Some points are improved. For instance, Proof of chaos propagation is improved,, using Hardy's inequalities, we improve our results when the state space contains two points, the complete garph study is generalised, we add comments on our coupling constructio