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

Author

Listed:
  • Michael Fleermann

    (FernUniversität in Hagen)

  • Werner Kirsch

    (FernUniversität in Hagen)

  • Gabor Toth

    (FernUniversität in Hagen)

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.

Suggested Citation

  • Michael Fleermann & Werner Kirsch & Gabor Toth, 2022. "Local Central Limit Theorem for Multi-group Curie–Weiss Models," Journal of Theoretical Probability, Springer, vol. 35(3), pages 2009-2019, September.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:3:d:10.1007_s10959-021-01122-4
    DOI: 10.1007/s10959-021-01122-4
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