Metastability and small eigenvalues in Markov chains

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 considerably greater precision than has so far been 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 of the convergence of the probability distribution of the metastable transition times to the exponential distribution.

• Publication year

  2000

• Venue

  Journal of Physics A

• Publication date

  2000-07-21

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1088/0305-4470/33/46/102arXiv cond-mat/0007343
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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