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2016

Mixing of the Glauber dynamics for the ferromagnetic Potts model

4 years 6 months ago
Mixing of the Glauber dynamics for the ferromagnetic Potts model
We present several results on the mixing time of the Glauber dynamics for sampling from the Gibbs distribution in the ferromagnetic Potts model. At a fixed temperature and interaction strength, we study the interplay between the maximum degree (∆) of the underlying graph and the number of colours or spins (q) in determining whether the dynamics mixes rapidly or not. We find a lower bound L on the number of colours such that Glauber dynamics is rapidly mixing if at least L colours are used. We give a closely-matching upper bound U on the number of colours such that with probability that tends to 1, the Glauber dynamics mixes slowly on random ∆-regular graphs when at most U colours are used. We show that our bounds can be improved if we restrict attention to certain types of graphs of maximum degree ∆, e.g. toroidal grids for ∆ = 4.
Magnus Bordewich, Catherine S. Greenhill, Viresh P
Added 09 Apr 2016
Updated 09 Apr 2016
Type Journal
Year 2016
Where RSA
Authors Magnus Bordewich, Catherine S. Greenhill, Viresh Patel
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