Fluctuation moments induced by conjugation with asymptotically liberating random matrix ensembles

TL;DR

This paper explores how conjugation by asymptotically liberating random matrix ensembles affects fluctuation moments of constant matrices, extending understanding of asymptotic free independence and higher order moments.

Contribution

It investigates the fluctuation and higher order moments induced by conjugation with specific asymptotically liberating ensembles, including those related to the Discrete Fourier Transform matrix.

Findings

Determines fluctuation moments for ensembles related to the DFT matrix.

Extends the theory of asymptotic free independence to higher order moments.

Provides explicit calculations for moments induced by certain random matrix ensembles.

Abstract

G. Anderson and B. Farrel showed that conjugation of constant matrices by asymptotically liberating random unitary matrices give rise to asymptotic free independence. Independent Haar-unitary random matrices and independent Haar-orthogonal random matrices are examples of asymptotically liberating ensembles. In this paper, we investigate the fluctuation moments, and higher order moments, induced on constant matrices by conjugation with asymptotically liberating ensembles. In particular, we determine fluctuation moments induced by an ensembles related to the Discrete Fourier Transform matrix.