The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
Fast convergence of the Glauber dynamics for sampling independent sets
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
Markov Chain Algorithms for Planar Lattice Structures
SIAM Journal on Computing
Torpid Mixing of Some Monte Carlo Markov Chain Algorithms in Statistical Physics
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
On Phase Transition in the Hard-Core Model on ${\mathbb Z}^d$
Combinatorics, Probability and Computing
Slow mixing of glauber dynamics via topological obstructions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Torpid mixing of local Markov chains on 3-colorings of the discrete torus
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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We show that local dynamics require exponential time for two sampling problems: independent sets on the triangular lattice (the hard-core lattice gas model) and weighted even orientations of the Cartesian lattice (the 8-vertex model). For each problem, there is a parameter 茂戮驴known as the fugacity such that local Markov chains are expected to be fast when 茂戮驴is small and slow when 茂戮驴is large. However, establishing slow mixing for these models has been a challenge because standard contour arguments typically used to show that a chain has small conductance do not seem sufficient. We modify this approach by introducing the notion of fat contoursthat can have nontrivial d-dimensional volume and use these to establish slow mixing of local chains defined for these models.