Non-Gaussian Random Matrix Models for Two-faced Families of Random Variables Having Bi-free Central Limit Distributions

TL;DR

This paper develops non-Gaussian random matrix models to approximate bi-free central limit distributions, demonstrating asymptotic bi-freeness under weaker conditions than independence.

Contribution

It introduces non-Gaussian random matrix models for bi-free distributions and proves their asymptotic bi-freeness with constant diagonal matrices.

Findings

Non-Gaussian matrices approximate bi-free distributions

Asymptotic bi-freeness established under weak conditions

Models extend beyond Gaussian assumptions

Abstract

In this paper, we construct random two-faced families of matrices with non-Gaussian entries to approximate a two-faced family of random variables having a bi-free central limit distribution. We prove that, under modest conditions weaker than independence, a family of random two-faced family of matrices with non-Gaussian entries is asymptotically bi-free from a two-faced family of constant diagonal matrices.