Metastability and small eigenvalues in Markov chains
Disordered Systems and Neural Networks
2009-10-31 v1
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.
Keywords
Cite
@article{arxiv.cond-mat/0007343,
title = {Metastability and small eigenvalues in Markov chains},
author = {A. Bovier and M. Eckhoff and V. Gayrard and M. Klein},
journal= {arXiv preprint arXiv:cond-mat/0007343},
year = {2009}
}
Comments
5pp, AMSTeX