Mixing of random walks and other diffusions on a graph
Surveys in combinatorics, 1995
Path coupling: A technique for proving rapid mixing in Markov chains
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Sampling adsorbing staircase walks using a new Markov chain decomposition method
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Combinatorial criteria for uniqueness of Gibbs measures
Random Structures & Algorithms
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We consider Glauber dynamics on finite spin systems. The mixing time of Glauber dynamics can be bounded in terms of the influences of sites on each other. We consider three parameters bounding these influences: α, the total influence on a site, as studied by Dobrushin; α′, the total influence of a site, as studied by Dobrushin and Shlosman; and α″, the total influence of a site in any given context, which is related to the path-coupling method of Bubley and Dyer. It is known that if any of these parameters is less than 1 then random-update Glauber dynamics (in which a randomly chosen site is updated at each step) is rapidly mixing. It is also known that the Dobrushin condition α q-colourings of a degree-Δ graph G when q ≥ 2Δ.