Uniform Convergence and the Central Limit Theorem

TL;DR

This paper establishes uniform convergence of densities in the free central limit theorem, removing the need for bounded support assumptions, thus broadening the theorem's applicability.

Contribution

It provides new results on uniform convergence in the free CLT without requiring bounded support, advancing theoretical understanding.

Findings

Proves uniform convergence of densities in free CLT

Removes bounded support assumption

Extends applicability of free CLT results

Abstract

We prove results about uniform convergence of densities in the free central limit theorem without assumptions of boundedness on the support.