On Markov chains for independent sets
Journal of Algorithms
Path coupling: A technique for proving rapid mixing in Markov chains
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Improved Bounds for Sampling Coloring
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Glauber Dynamics onTrees and Hyperbolic Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Fast mixing for independent sets, colorings and other models on trees
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Mixing in time and space for lattice spin systems: A combinatorial view
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part II
Fast mixing for independent sets, colorings and other models on trees
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Counting without sampling: new algorithms for enumeration problems using statistical physics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Fast mixing for independent sets, colorings, and other models on trees
Random Structures & Algorithms
Random Structures & Algorithms
Dobrushin conditions and systematic scan
Combinatorics, Probability and Computing
Approximating partition functions of the two-state spin system
Information Processing Letters
Dobrushin conditions and systematic scan
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Sampling colourings of the triangular lattice
Random Structures & Algorithms
Dobrushin conditions for systematic scan with block dynamics
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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We generalize previously known conditions for uniqueness of the Gibbs measure in statistical physics models by presenting conditions of any finite size for models on any underlying graph. We give two dual conditions, one requiring that the total influence on a site is small, and the other that the total influence of a site is small. Our proofs are combinatorial in nature and use tools from the analysis of discrete Markov chains, in particular the path coupling method. The implications of our conditions for the mixing time of natural Markov chains associated with the models are discussed as well. We also present some examples of models for which the conditions hold. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005