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

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

2002-11-08

arxiv.org/abs/cond-mat/0211166v1

J. Phys. A: Math. Gen. 36, 3647 (2003).

Physics

Condensed Matter

Statistical Mechanics

To be submitted to J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/36/13/301

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.

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