WIAS Preprint No. 600, (2000)

Metastability and small eigenvalues in Markov chains


  • Bovier, Anton
  • Eckhoff, Michael
  • Gayrard, Véronique
  • Klein, Markus

2010 Mathematics Subject Classification

  • 60J10 60K35


  • Markov chains, metastability, eigenvalue problems, exponential distribution




In this letter we announce rigorous results that elucidate the relation between metastable 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.

Appeared in

  • J. Phys A 33, (2000), L447-L451

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