In this survey paper, we describe and characterize an extension to theclassical path coupling method applied statistical mechanical models, referredto as aggregate path coupling. In conjunction with large deviations estimates,we use this aggregate path coupling method to prove rapid mixing of Glauberdynamics for a large class of statistical mechanical models, including modelsthat exhibit discontinuous phase transitions which have traditionally been moredifficult to analyze rigorously. The parameter region for rapid mixing for thegeneralized Curie-Weiss-Potts model is derived as a new application of theaggregate path coupling method.
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