Local Central Limit Theorem for Multi-Group Curie-Weiss Models

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.

References in corpus (3)

• Macroscopic limit of a bipartite Curie-Weiss model: a dynamical approach
• Fluctuation results for general block spin Ising models
• Multi-group Binary Choice with Social Interaction and a Random Communication Structure -- a Random Graph Approach

Cited by in corpus (2)

• Local Central Limit Theorem for Long-Range Two-Body Potentials at Sufficiently High Temperatures
• Interval Type Local Limit Theorems for Lattice Type Random Variables and Distributions