Title: Metastable Markov chains: from the convergence of the trace to the convergence of the finite-dimensional distributions,
Abstract: We consider continuous-time Markov chains which display a family of wells at
the same depth. We provide sufficient conditions which entail the convergence
of the finite-dimensional distributions of the order parameter to the ones of a
finite state Markov chain. We also show that the state of the process can be
represented as a time-dependent convex combination of metastable states, each
of which is supported on one well.