Abstract. We propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible Markov chains on finite state sets. Spectral gaps are a common tool for evaluating convergence rates of Markov chains. As an illustration, we successfully use this technique to evaluate the 'absorption time' of the 'Backgammon model', a paradigmatic model for glassy dynamics. We also discuss the application of this technique to the 'contingency table problem', a notoriously difficult problem from probability theory. The interest of this technique is that it connects spectral gaps, which are quantities related to dynamics, with static quantities, calculated at equilibrium.

PACS numbers: 02.50.Ga, 05.40.−a, 05.10.Ln

Print publication: Issue 13 (4 April 2003)
Received 15 November 2002, in final form 6 February 2003
Published 19 March 2003