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

Fluctuation moments induced by conjugation with asymptotically liberating random matrix ensembles