On metastability

Laurent Miclo ()
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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, IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Metastability; Finite absorbing Markov process; Exit time; Exit position; Spectral quantitative criterion; First Dirichlet eigenvalue; Quasi-stationary distribution; Poisson equation; Eigentime identity; Small temperature (search for similar items in EconPapers)
Date: 2022-06-10
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Published in Probability Theory and Related Fields, 2022, 184 (1-2), pp.275-322. ⟨10.1007/s00440-022-01147-8⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04050023

DOI: 10.1007/s00440-022-01147-8

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