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Metastability and small eigenvalues in Markov chains

A. Bovier·M. Eckhoff·V. Gayrard·M. Klein
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Abstract

In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state, and sharp estimates on the convergence of probability distribution of the metastable transition times to the exponential distribution.

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A. Bovier, M. Eckhoff, V. Gayrard, M. Klein. 2000-07-21. Metastability and small eigenvalues in Markov chains. https://doi.org/10.1088/0305-4470%2F33%2F46%2F102

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