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
The Glauber dynamics on colourings of a graph with high girth and maximum degree
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Randomly coloring graphs of girth at least five
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Randomly Colouring Graphs with Lower Bounds on Girth and Maximum Degree
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A Non-Markovian Coupling for Randomly Sampling Colorings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Randomly Coloring Constant Degree Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Mixing in time and space for discrete spin systems
Mixing in time and space for discrete spin systems
A second threshold for the hard-core model on a Bethe lattice
Random Structures & Algorithms - Isaac Newton Institute Programme “Computation, Combinatorics and Probability”: Part I
Combinatorial criteria for uniqueness of Gibbs measures
Random Structures & Algorithms
Randomly coloring planar graphs with fewer colors than the maximum degree
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Reconstruction for the Potts model
Proceedings of the forty-first annual ACM symposium on Theory of computing
The Glauber Dynamics for Colourings of Bounded Degree Trees
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Phase transition for the mixing time of the Glauber dynamics for coloring regular trees
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Rapid mixing of subset Glauber dynamics on graphs of bounded tree-width
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Approximate counting via correlation decay in spin systems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Phase transition for Glauber dynamics for independent sets on regular trees
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We study the mixing time of the Glauber dynamics for general spin systems on the regular tree, including the Ising model, the hard-core model (independent sets), and the antiferromagnetic Potts model at zero temperature (colorings). We generalize a framework, developed in our recent paper (Martinelli, Sinclair, and Weitz, Tech. Report UCB//CSD-03-1256, Dept. of EECS, UC Berkeley, July 2003) in the context of the Ising model, for establishing mixing time O(nlog n), which ties this property closely to phase transitions in the underlying model. We use this framework to obtain rapid mixing results for several models over a significantly wider range of parameter values than previously known, including situations in which the mixing time is strongly dependent on the boundary condition. We also discuss applications of our framework to reconstruction problems on trees. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007 A preliminary version of this paper appeared in Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms, January 2004. This work was done while the author was visiting the Departments of EECS and Statistics, University of California, Berkeley, supported in part by a Miller Visiting Professorship.