Limit theorems for the empirical vector of the Curie-Weiss-Potts model
type: Item
instance of: scholarly article
title: Limit theorems for the empirical vector of the Curie-Weiss-Potts model
zbMATH Open document ID: 0705.60027
DOI: 10.1016/0304-4149(90)90122-9
author: Richard S. Ellis
author: Kongming Wang
published in: Stochastic Processes and their Applications
publication date: 1990-01-01T00:00:00Z
review text: Limit theorems for the empirical vector \(L_ n\) of spin random variables with a parameter of dependence \(\beta\) in the Curie-Weiss-Potts-Ising model of statistical mechanics in both non-critical and critical cases are obtained, including some earlier results of \textit{R. S. Ellis, C. M. Newman} and \textit{J. S. Rosen} [Z. Wahrscheinlichkeitstheorie Verw. Gebiete 44, 117-139 (1978; Zbl 0364.60120), and ibid. 51, 153-169 (1980; Zbl 0404.60096)]. The limit theorems state the law of large numbers \(L_ n\to \delta_{\nu^ 0}\), \(n\to \infty\), with \(\nu^ 0=(q^{-1},...,q^{- 1})\), and the number of spin states q, in the sub-critical case \(\beta <\beta_ C\), and its breakdown in critical and super-critical cases \(\beta \geq \beta_ C\), and the central limits for (\(\sqrt{n}L_ n)\) compensated.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 4157590
zbMATH Keywords: law of large numbers
zbMATH Keywords: Curie-Weiss-Potts-Ising model
zbMATH Keywords: statistical mechanics
zbMATH Keywords: sub-critical case
zbMATH Keywords: super-critical cases
zbMATH Keywords: central limits
reviewed by: Evgeni Trofimov
MaRDI profile type: Publication
full work available at URL: 0304-4149(90)90122-9
OpenAlex ID: W2056664585
cites work: Asymptotics of maximum likelihood estimators for the Curie-Weiss model
cites work: On limit theorems for the bivariate (magnetization, energy) variable at the critical point
cites work: Symmetry breaking and random waves for magnetic systems on a circle
cites work: Q3681702
cites work: Limit theorems for sums of dependent random variables occurring in statistical mechanics
cites work: Large deviations for the empirical field of curie-weiss models∗
Recommended article: Limit theorems for maximum likelihood estimators in the Curie-Weiss-Potts model
Recommended article: Limit theorems and coexistence probabilities for the Curie-Weiss Potts model with an external field
Recommended article: Limit theorems for multi-group Curie-Weiss models via the method of moments
Recommended article: Limit theorems for the bipartite Potts model
Recommended article: Large deviations for the empirical field of curie-weiss models∗
Recommended article: Bounds on convergence for the empirical vector of the Curie-Weiss-Potts model with a non-zero external field vector
Recommended article: Q5719305
Recommended article: Large deviations principle for Curie–Weiss models with random fields
description: scientific article; zbMATH DE number 4157590