  The purpose of this paper is to extend the investigation of the Fleming-Viot
process in discrete space started in a previous work to two specific examples.
The first one corresponds to a random walk on the complete graph. Due to its
geometry, we establish several explicit and optimal formulas for the
Fleming-Viot process (invariant distribution, correlations, spectral gap). The
second example corresponds to a Markov chain in a two state space. In this
case, the study of the Fleming-Viot particle system is reduced to the study of
birth and death process with quadratic rates.
