Professor Magnus Bordewich m.j.r.bordewich@durham.ac.uk
Professor
Mixing of the Glauber Dynamics for the Ferromagnetic Potts Model
Bordewich, Magnus; Greenhill, Catherine; Patel, Viresh
Authors
Catherine Greenhill
Viresh Patel
Abstract
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 (Δ) 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 Δ-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 Δ, e.g. toroidal grids for Δ = 4.
Citation
Bordewich, M., Greenhill, C., & Patel, V. (2016). Mixing of the Glauber Dynamics for the Ferromagnetic Potts Model. Random Structures and Algorithms, 48(1), 21-52. https://doi.org/10.1002/rsa.20569
Journal Article Type | Article |
---|---|
Acceptance Date | Apr 14, 2014 |
Online Publication Date | Sep 4, 2014 |
Publication Date | Jan 1, 2016 |
Deposit Date | Apr 24, 2015 |
Publicly Available Date | Sep 23, 2015 |
Journal | Random Structures and Algorithms |
Print ISSN | 1042-9832 |
Publisher | Wiley |
Peer Reviewed | Peer Reviewed |
Volume | 48 |
Issue | 1 |
Pages | 21-52 |
DOI | https://doi.org/10.1002/rsa.20569 |
Keywords | Glauber dynamics, Mixing time, Potts model, Ferromagnetic. |
Related Public URLs | http://arxiv.org/abs/1305.0776 |
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Advance online version © 2015 The Authors Random Structures & Algorithms Published by Wiley Periodicals, Inc. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Published Journal Article (Final published version)
(250 Kb)
PDF
Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
Final published version
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