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Limit theorems for the empirical vector of the Curie-Weiss-Potts model

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  • Ellis, Richard S.
  • Wang, Kongming

Abstract

The law of large numbers and its breakdown, the central limit theorem, a central limit theorem with conditioning, and a central limit theorem with random centering are proved for the empirical vector of the Curie-Weiss-Potts model, which is a model in statistical mechanics. The nature of the limits reflects the phase transition in the model.

Suggested Citation

  • Ellis, Richard S. & Wang, Kongming, 1990. "Limit theorems for the empirical vector of the Curie-Weiss-Potts model," Stochastic Processes and their Applications, Elsevier, vol. 35(1), pages 59-79, June.
    • Handle: RePEc:eee:spapps:v:35:y:1990:i:1:p:59-79
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    Citations

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    Cited by:

    1. Gandolfo, Daniel & Ruiz, Jean & Wouts, Marc, 2010. "Limit theorems and coexistence probabilities for the Curie-Weiss Potts model with an external field," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 84-104, January.
    2. 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.
    3. Andrea Cerioli, 2002. "Testing Mutual Independence Between Two Discrete-Valued Spatial Processes: A Correction to Pearson Chi-Squared," Biometrics, The International Biometric Society, vol. 58(4), pages 888-897, December.
    4. Cerioli, Andrea, 2002. "Tests of homogeneity for spatial populations," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 123-130, June.
    5. Martschink, Bastian, 2014. "Bounds on convergence for the empirical vector of the Curie–Weiss–Potts model with a non-zero external field vector," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 118-126.
    6. 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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