We study the convergence to equilibrium of n-samples of independent Markovchains in discrete and continuous time. They are defined as Markov chains on the n-fold Cartesian product of the initial state space by itself, and they converge to the direct product of n copies of the initial stationary distribution. Sharp estimates for the convergence speed are given in terms of the spectrum of the initial chain. A cutoff phenomenon occurs in thesense that as n tends to infinity, the total variation distancebetween the distribution of the chain and the asymptotic distribution tendsto 1 or 0 at all times. As an application,an algorithm is proposed for producing an n-sample of the asymptotic distribution of the initial chain, with an explicit stopping test.
