A simple invariance theorem

TL;DR

This paper extends Lindeberg's argument to establish a general invariance theorem, enabling applications across random matrix theory, spin glasses, and maxima of random fields.

Contribution

It introduces a straightforward extension of Lindeberg's method to prove a broad invariance principle applicable in various complex probabilistic models.

Findings

Proved a general invariance theorem using an extended Lindeberg approach.

Applied the invariance result to random matrix theory, spin glasses, and random fields.

Demonstrated the versatility of the technique across different domains.

Abstract

We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.