Proceedings of 37th Conference on Foundations of Computer Science (1996)
Oct. 14, 1996 to Oct. 16, 1996
N. Madras , Dept. of Math. & Stat., York Univ., North York, Ont., Canada
D. Randall , Dept. of Math. & Stat., York Univ., North York, Ont., Canada
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.
Markov processes; mixing rate bounding; Markov chain; state space decomposition; Monte Carlo Markov chain algorithm; random three-colorings; 2-dimensional lattice regions; 3-state Potts model; ice model; statistical mechanics; Metropolis sampling algorithm; factorization theorems
D. Randall and N. Madras, "Factoring graphs to bound mixing rates," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 194.