Joint Global Fluctuations of complex Wigner and deterministic Matrices (2010.02963v1)

Published 6 Oct 2020 in math.PR and math.OA

Abstract: We characterize the limiting fluctuations of traces of several independent Wigner matrices and deterministic matrices under mild conditions. A CLT holds but in general the families are not asymptotically free of second order and the limiting covariance depends on more information on the deterministic matrices than their limiting *-distribution.

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