  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.
