  In many situations it is important to be able to propose $N$ independent
realizations of a given distribution law. We propose a strategy for making $N$
parallel Monte Carlo Markov Chains (MCMC) interact in order to get an
approximation of an independent $N$-sample of a given target law. In this
method each individual chain proposes candidates for all other chains. We prove
that the set of interacting chains is itself a MCMC method for the product of
$N$ target measures. Compared to independent parallel chains this method is
more time consuming, but we show through concrete examples that it possesses
many advantages: it can speed up convergence toward the target law as well as
handle the multi-modal case.
