Random generation of embedded graphs and an extension to Dobrushin uniqueness (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Decomposition Methods and Sampling Circuits in the Cartesian Lattice
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Disjoint Decomposition of Markov Chains and Sampling Circuits in Cayley Graphs
Combinatorics, Probability and Computing
Undirected connectivity in log-space
Journal of the ACM (JACM)
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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.