Joint convergence of several copies of different patterned random matrices

TL;DR

This paper investigates the joint convergence behavior of multiple independent patterned random matrices, revealing asymptotic freeness between Wigner matrices and other patterned matrices in noncommutative probability.

Contribution

It establishes joint convergence for various patterned matrices and demonstrates asymptotic freeness between Wigner matrices and other matrix types.

Findings

Joint convergence holds for Wigner, Toeplitz, Hankel, reverse circulant, and symmetric circulant matrices.

Wigner matrices become asymptotically free from other patterned matrices.

The paper explores properties of the limiting distributions.

Abstract

We study the joint convergence of independent copies of several patterned matrices in the noncommutative probability setup. In particular, joint convergence holds for the well known Wigner, Toeplitz, Hankel, reverse circulant and symmetric circulant matrices. We also study some properties of the limits. In particular, we show that copies of Wigner becomes asymptotically free with copies of any of the above other matrices.