Metastability and small eigenvalues in Markov chains

Details Metastability and small eigenvalues in Markov chains Metastability and small eigenvalues in Markov chains

2000-07-21

arxiv.org/abs/cond-mat/0007343v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

5pp, AMSTeX

Scientific paper

10.1088/0305-4470/33/46/102

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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