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Bounds on convergence for the empirical vector of the Curie–Weiss–Potts model with a non-zero external field vector

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  • Martschink, Bastian

Abstract

In the present paper we obtain rates of convergence for limit theorems via Stein’s Method of exchangeable pairs in the context of the Curie–Weiss–Potts model and we consider only the case of non-zero external field h∈Rq. Our interest is in the limit distribution of the empirical vector of the spin variables and we obtain bounds for multivariate normal approximation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:88:y:2014:i:c:p:118-126
    DOI: 10.1016/j.spl.2014.01.033
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    References listed on IDEAS

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    1. Rinott, Yosef & Rotar, Vladimir, 1996. "A Multivariate CLT for Local Dependence withn-1/2 log nRate and Applications to Multivariate Graph Related Statistics," Journal of Multivariate Analysis, Elsevier, vol. 56(2), pages 333-350, February.
    2. Wang, Kongming, 1994. "Solutions of the variational problem in the Curie--Weiss--Potts model," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 245-252, April.
    3. 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.
    4. 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.
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