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

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• 作者：Yevgeniy Kovchegov ; Peter T. Otto
• 关键词：Mixing times ; Glauber dynamics ; Gibbs ensemble ; Equilibrium phase transition ; Path coupling ; Curie–Weiss–Potts model ; Primary 60J10 ; Secondary 60K35
• 刊名：Journal of Statistical Physics
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：161
• 期：3
• 页码：553-576
• 全文大小：567 KB
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• 作者单位：Yevgeniy Kovchegov (1)
  Peter T. Otto (2)
  
  1. Department of Mathematics, Oregon State University, Corvallis, OR, 97331, USA
  2. Department of Mathematics, Willamette University, Salem, OR, 97302, USA
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Statistical Physics
  Mathematical and Computational Physics
  Physical Chemistry
  Quantum Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9613

文摘

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. Keywords Mixing times Glauber dynamics Gibbs ensemble Equilibrium phase transition Path coupling Curie–Weiss–Potts model