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Limit theorems for maximum likelihood estimators in the Curie-Weiss-Potts model

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  • Ellis, Richard S.
  • Wang, Kongming

Abstract

The Curie-Weiss-Potts model, a model in statistical mechanics, is parametrized by the inverse temperature [beta] and the external magnetic field h. This paper studies the asymptotic behavior of the maximum likelihood estimator of the parameter [beta] when h = 0 and the asymptotic behavior of the maximum likelihood estimator of the parameter h when [beta] is known and the true value of h is 0. The limits of these maximum likelihood estimators reflect the phase transition in the model; i.e., different limits depending on whether [beta] [beta]c, where [beta]c [epsilon] (0, [infinity]) is the critical inverse temperature of the model.

Suggested Citation

  • Ellis, Richard S. & Wang, Kongming, 1992. "Limit theorems for maximum likelihood estimators in the Curie-Weiss-Potts model," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 251-288, March.
    • Handle: RePEc:eee:spapps:v:40:y:1992:i:2:p:251-288
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    Cited by:

    1. Nardi, Francesca R. & Zocca, Alessandro, 2019. "Tunneling behavior of Ising and Potts models in the low-temperature regime," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4556-4575.
    2. Bet, Gianmarco & Gallo, Anna & Nardi, F.R., 2024. "Metastability for the degenerate Potts Model with positive external magnetic field under Glauber dynamics," Stochastic Processes and their Applications, Elsevier, vol. 172(C).

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