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

Claudio Landim; Michail Loulakis; Mustapha Mourragui

doi:10.1214/18-ejp220

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arXiv · 1703.09481

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

Claudio Landim·Michail Loulakis·Mustapha Mourragui

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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.

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Claudio Landim, Michail Loulakis, Mustapha Mourragui. 2017-03-28. Metastable Markov chains: from the convergence of the trace to the convergence of the finite-dimensional distributions. https://doi.org/10.1214/18-ejp220

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