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Metastable Markov chains: from the convergence of the trace to the convergence of the finite-dimensional distributions. (English) Zbl 1414.60080
Summary: 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.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J27 Continuous-time Markov processes on discrete state spaces
82C22 Interacting particle systems in time-dependent statistical mechanics
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