Local Central Limit Theorem for Multi-Group Curie-Weiss Models
Probability
2022-08-09 v1 Mathematical Physics
math.MP
Abstract
We define a multi-group version of the mean-field spin 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 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
Cite
@article{arxiv.2012.08349,
title = {Local Central Limit Theorem for Multi-Group Curie-Weiss Models},
author = {Michael Fleermann and Werner Kirsch and Gabor Toth},
journal= {arXiv preprint arXiv:2012.08349},
year = {2022}
}