On the local central limit theorem for interacting spin systems

TL;DR

This paper establishes the equivalence between integral and local central limit theorems for interacting spin systems with absolutely summable pair potentials, regardless of temperature conditions.

Contribution

It proves the equivalence between integral and local CLT for spin systems with no temperature restrictions, broadening theoretical understanding.

Findings

Proves equivalence of integral and local CLT for spin systems

Applies to systems with absolutely summable pair potentials

No temperature restrictions required

Abstract

We prove the equivalence between integral and local central limit theorem for spin system interacting via an absolutely summable pair potential without any conditions on the temperature of the system.