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Rapid Mixing of Glauber Dynamics of Gibbs Ensembles via Aggregate Path Coupling and Large Deviations Methods

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Abstract

In this paper, we present a novel extension to the classical path coupling method to statistical mechanical models which we refer to as aggregate path coupling. In conjunction with large deviations estimates, we use this aggregate path coupling method to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibit discontinuous phase transitions which have traditionally been more difficult to analyze rigorously. The parameter region for rapid mixing for the generalized Curie–Weiss–Potts model is derived as a new application of the aggregate path coupling method.

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Acknowledgments

This work was partially supported by a grant from the Simons Foundation (#284262 to Yevgeniy Kovchegov).

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Authors and Affiliations

  1. Department of Mathematics, Oregon State University, Corvallis, OR, 97331, USA

    Yevgeniy Kovchegov

  2. Department of Mathematics, Willamette University, Salem, OR, 97302, USA

    Peter T. Otto

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  1. Yevgeniy Kovchegov
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  2. Peter T. Otto
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Correspondence to Peter T. Otto.

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Kovchegov, Y., Otto, P.T. Rapid Mixing of Glauber Dynamics of Gibbs Ensembles via Aggregate Path Coupling and Large Deviations Methods. J Stat Phys 161, 553–576 (2015). https://doi.org/10.1007/s10955-015-1345-3

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  • DOI: https://doi.org/10.1007/s10955-015-1345-3

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