Scaling Limits for Multispecies Statistical Mechanics Mean-Field Models

TL;DR

This paper investigates the asymptotic behavior of multi-species Curie-Weiss models, identifying conditions under which the sums of spins converge to Gaussian or exponential distributions and calculating the covariance structure.

Contribution

It provides new conditions for the limiting distributions of normalized sums in multi-species mean-field models and explicitly computes the covariance matrix based on model parameters.

Findings

Limiting distributions can be Gaussian or exponential.

Explicit covariance matrix formulas derived.

Conditions for different limiting behaviors established.

Abstract

We study the limiting thermodynamic behavior of the normalized sums of spins in multi-species Curie-Weiss models. We find sufficient conditions for the limiting random vector to be Gaussian (or to have an exponential distribution of higher order) and compute the covariance matrix in terms of model parameters.