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Factoring graphs to bound mixing rates

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2 Author(s)
N. Madras ; Dept. of Math. & Stat., York Univ., North York, Ont., Canada ; D. Randall

This paper develops a new technique for bounding the mixing rate of a Markov chain by decomposing the state space into factors. The first application is an efficient Monte Carlo Markov chain algorithm for generating random three-colorings of 2-dimensional lattice regions. This provides a rigorous tool for studying some properties of the 3-state Potts model and the ice model from statistical mechanics. As a second application, we develop similar techniques to bound the mixing rate of a Metropolis sampling algorithm by a type of “temperature factorization”. Both factorization theorems work by using known mixing properties of related Markov chains to establish the efficiency of a new sampling algorithm

Published in:

Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on

Date of Conference:

14-16 Oct 1996