Fluctuation Moments Induced by Conjugation with Asymptotically Liberating Random Matrix Ensembles

Independent Haar-unitary random matrices and independent Haar-orthogonal are known to be asymptotically liberating ensembles, they give rise asymptotic free independence when used for conjugation of constant matrices. G. Anderson B. Farrel showed that a certain family discrete unitary can actually the same end. In this paper, we investigate fluctuation moments higher-order induced on by with ensembles. We show first time associated second-order obtained from an ensemble consisting signed permutation Fourier transform matrix. also determine various related ensembles where do not get expressions but others traffic independence.