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
Glauber Dynamics onTrees and Hyperbolic Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
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
The Ising Model on Trees: Boundary Conditions and Mixing Time
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
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
Combinatorial criteria for uniqueness of Gibbs measures
Random Structures & Algorithms
Counting independent sets up to the tree threshold
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Optimal phylogenetic reconstruction
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Reconstruction threshold for the hardcore model
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
The effect of boundary conditions on mixing rates of markov chains
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
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We study the mixing time of the Glauber dynamics for general spin systems on bounded-degree trees, 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 [18] in the context of the Ising model, for establishing mixing time O(n log 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.