Metastable Markov chains: from the convergence of the trace to the convergence of the finite-dimensional distributions

International audienceWe consider continuous-time Markov chains which display a family of wells at the same depth. We show that in an appropriate time-scale the state of the process can be represented as a time-dependent convex combination of mestastable states, each of which is supported on one well. The time dependence of the convex combination is given in terms of the distribution of a reduced Markov chain