Glauber Dynamics onTrees and Hyperbolic Graphs
FOCS '01 Proceedings of the 42nd 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
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
Combinatorial criteria for uniqueness of Gibbs measures
Random Structures & Algorithms
A simple condition implying rapid mixing of single-site dynamics on spin systems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Stopping times, metrics and approximate counting
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
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
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We study the mixing time of systematic scan Markov chains on finite spin systems. It is known that, in a single site setting, the mixing time of systematic scan can be bounded in terms of the influences sites have on each other. We generalise this technique for bounding the mixing time of systematic scan to block dynamics, a setting in which a set of sites are updated simultaneously. In particular we present a parameter α, representing the maximum influence on any site, and show that if α O(log n) mixing of a systematic scan for proper q-colourings of a general graph with maximum vertex-degree Δ whenever q ≥ 2Δ. We also apply the method to improve the number of colours required in order to obtain mixing in O(log n) scans for a systematic scan colouring of trees.