• Abstract:   We present a new technique for constructing and analyzing couplings to bound the convergence rate of finite Markov chains. Our main theorem is a generalization of the path coupling theorem of Bubley and Dyer, allowing the defining partial couplings to have length determined by a random stopping time. Unlike the original path coupling theorem, our version can produce multi-step (non-Markovian) couplings. Using our variable length path coupling theorem, we improve the upper bound on the mixing time of the Glauber dynamics for randomly sampling colorings.

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Full version of Jan 9, 2005, 18pp.	PDF	PostScript	DVI
SODA Proceedings version, Oct. 5, 2003, 8pp.	Available by request.
Previous release, July 3, 2003, 11pp.	Available by request.