Analyzing Glauber dynamics by comparison of Markov chains

  • Dana Randall
  • Prasad Tetali
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1380)


A popular technique for studying random properties of a combinatorial set is to design a Markov chain Monte Carlo algorithm. For many problems there are natural Markov chains connecting the set of allowable configurations which are based on local moves, or “Glauber dynamics.” Typically these single site update algorithms are difficult to analyze, so often the Markov chain is modified to update several sites simultaneously. Recently there has been progress in analyzing these more complicated algorithms for several important combinatorial problems.

In this work we use the comparison technique of Diaconis and Saloff-Coste to show that several of the natural single point update algorithms are efficient. The strategy is to relate the mixing rate of these algorithms to the corresponding non-local algorithms which have already been analyzed. This allows us to give polynomial bounds for single point update algorithms for problems such as generating tilings, colorings and independent sets.


Markov Chain Comparison Theorem Triangular Lattice Dirichlet Form Markov Chain Monte Carlo Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Dana Randall
    • 1
  • Prasad Tetali
    • 2
  1. 1.School of Mathematics and College of ComputingGeorgia Institute of TechnologyAtlantaUSA
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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