On rates of convergence in the Curie–Weiss–Potts model with an external field
Annales de l'I.H.P. Probabilités et statistiques, Volume 51 (2015) no. 1, p. 252-282

In the present paper we obtain rates of convergence for the limit theorems of the density vector in the Curie–Weiss–Potts model via Stein’s Method of exchangeable pairs. Our results include Kolmogorov bounds for multivariate normal approximation in the whole domain β0 and h0, where β is the inverse temperature and h an exterior field. In this model, the critical line β=β c (h) is explicitly known and corresponds to a first order transition. We include rates of convergence for non-Gaussian approximations at the extremity of the critical line of the model.

Dans cet article, nous obtenons des taux de convergence pour les vecteurs de densité dans le modèle de Curie–Weiss–Potts via la méthode de Stein des paires échangeables. Nos résultats incluent des bornes de Kolmogorov pour l’approximation normale multivariée dans tout le domaine β0 et h0, où β est l’inverse de la température et h un champ extérieur. Dans ce modèle, la ligne critique β=β c (h) est explicitement connue et correspond à une transition du premier ordre. Nous incluons des taux de convergence pour des approximations non-gaussiennes au bord de la ligne critique du modèle.

DOI : https://doi.org/10.1214/14-AIHP599
Classification:  60F05,  82B20,  82B26
Keywords: Stein’s method, exchangeable pairs, Curie–Weiss–Potts models, critical temperature
@article{AIHPB_2015__51_1_252_0,
     author = {Eichelsbacher, Peter and Martschink, Bastian},
     title = {On rates of convergence in the Curie--Weiss--Potts model with an external field},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {51},
     number = {1},
     year = {2015},
     pages = {252-282},
     doi = {10.1214/14-AIHP599},
     zbl = {06412904},
     mrnumber = {3300970},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2015__51_1_252_0}
}
Eichelsbacher, Peter; Martschink, Bastian. On rates of convergence in the Curie–Weiss–Potts model with an external field. Annales de l'I.H.P. Probabilités et statistiques, Volume 51 (2015) no. 1, pp. 252-282. doi : 10.1214/14-AIHP599. http://www.numdam.org/item/AIHPB_2015__51_1_252_0/

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