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We propose an exact technique to calculate lower bounds of spectral gaps ofdiscrete time reversible Markov chains on finite state sets. Spectral gaps area common tool for evaluating convergence rates of Markov chains. As anillustration, we successfully use this technique to evaluate the ``absorptiontime'' of the ``Backgammon model'', a paradigmatic model for glassy dynamics.We also discuss the application of this technique to the ``Contingency tableproblem'', a notoriously difficult problem from probability theory. Theinterest of this technique is that it connects spectral gaps, which arequantities related to dynamics, with static quantities, calculated atequilibrium.Comment: To be submitted to J. Phys. A: Math. Ge

Bounding spectral gaps of Markov chains: a novel exact multi-decomposition technique