  Consider a continuous time Markov chain with rates Q in the state space
\Lambda\cup\{0\} with 0 as an absorbing state. In the associated Fleming-Viot
process N particles evolve independently in \Lambda with rates Q until one of
them attempts to jump to the absorbing state 0. At this moment the particle
comes back to \Lambda instantaneously, by jumping to one of the positions of
the other particles, chosen uniformly at random. When \Lambda is finite, we
show that the empirical distribution of the particles at a fixed time converges
as N\to\infty to the distribution of a single particle at the same time
conditioned on non absorption. Furthermore, the empirical profile of the unique
invariant measure for the Fleming-Viot process with N particles converges as
N\to\infty to the unique quasi-stationary distribution of the one-particle
motion. A key element of the approach is to show that the two-particle
correlations is of order 1/N.
