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Keywords:

  • random sampling;
  • Markov Chain Monte Carlo;
  • path coupling;
  • non-Markovian coupling

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 multistep (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. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007