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On metastability

Author

Listed:
  • Laurent Miclo

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CNRS - Centre National de la Recherche Scientifique, UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse)

Abstract

Consider finite state space irreducible and absorbing Markov processes. A general spectral criterion is provided for the absorbing time to be close to an exponential random variable, whatever the starting point. When exiting points are added to the state space, our criterion also insures that the exit time and position are almost independent. Since this is valid for any exiting extension of the state space, it corresponds to an instance of the metastability phenomenon. Simple examples at small temperature suggest that this new spectral criterion is quite sharp. But the main interest of the underlying quantitative approach, based on Poisson equations, is that it does not rely on a small parameter such as temperature, nor on reversibility.

Suggested Citation

  • Laurent Miclo, 2022. "On metastability," Post-Print hal-04050023, HAL.
    • Handle: RePEc:hal:journl:hal-04050023
    DOI: 10.1007/s00440-022-01147-8
    as

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