LIMIT-THEOREMS FOR MAXIMUM-LIKELIHOOD ESTIMATORS IN THE CURIE-WEISS-POTTS MODEL

Authors

RS Ellis, University of Massachusetts - AmherstFollow
KM WANG

Publication Date

1992

Journal or Book Title

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Abstract

The Curie-Weiss-Potts model, a model in statistical mechanics, is parametrized by the inverse temperature β and the external magnetic field h. This paper studies the asymptotic behavior of the maximum likelihood estimator of the parameter β when h = 0 and the asymptotic behavior of the maximum likelihood estimator of the parameter h when β 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 β < β_c, β = β_c or β > β_c, where β_c ε (0, ∞) is the critical inverse temperature of the model.

Comments

The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1B-45F5GSC-1Y&_user=1516330&_coverDate=03%2F31%2F1992&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1699829463&_rerunOrigin=google&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=335d296f439171b15989d9e73f9673ab&searchtype=a

Pages

251-288

Volume

40

Issue

2

Recommended Citation

Ellis, RS and WANG, KM, "LIMIT-THEOREMS FOR MAXIMUM-LIKELIHOOD ESTIMATORS IN THE CURIE-WEISS-POTTS MODEL" (1992). STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 345.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/345