Local Central Limit Theorem for Multi-group Curie–Weiss Models

Michael Fleermann (), Werner Kirsch () and Gabor Toth ()
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Michael Fleermann: FernUniversität in Hagen
Werner Kirsch: FernUniversität in Hagen
Gabor Toth: FernUniversität in Hagen

Journal of Theoretical Probability, 2022, vol. 35, issue 3, 2009-2019

Abstract: Abstract We study a multi-group version of the mean-field Ising model, also called Curie–Weiss model. It is known that, in the high-temperature regime of this model, a central limit theorem holds for the vector of suitably scaled group magnetisations, that is, for the sum of spins belonging to each group. In this article, we prove a local central limit theorem for the group magnetisations in the high-temperature regime.

Keywords: Curie–Weiss model; Mean-field model; Local limit theorem; 60F05; 82B20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01122-4

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