Two Groups in a Curie–Weiss Model with Heterogeneous Coupling

Werner Kirsch () and Gabor Toth ()
Additional contact information
Werner Kirsch: FernUniversität Hagen
Gabor Toth: FernUniversität Hagen

Journal of Theoretical Probability, 2020, vol. 33, issue 4, 2001-2026

Abstract: Abstract We discuss a Curie–Weiss model with two groups with different coupling constants within and between groups. For the total magnetisations in each group, we show bivariate laws of large numbers and a central limit theorem which is valid in the high-temperature regime. In the critical regime, the total magnetisation normalised by $$N^{3/4}$$ N 3 / 4 converges to a non-trivial distribution which is not Gaussian, just as in the single-group Curie–Weiss model. Finally, we prove a kind of a ‘law of large numbers’ in the low-temperature regime, more precisely we prove that the empirical magnetisation converges in distribution to a mixture of two Dirac measures.

Keywords: Curie–Weiss; Central limit theorems; Multi-population models; 60F05; 82B20 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-019-00933-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:33:y:2020:i:4:d:10.1007_s10959-019-00933-w

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-019-00933-w

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().