Fluctuations of the spectrum of symmetrically deformed unitary invariant random matrix ensemble

Abstract

We consider an ensemble of n × n Hermitian random matrices being a generalization of the additive and multiplicative deformed unitary invariant ensembles. We express the limiting normalized counting measure (NCM) of eigenvalues via the NCMs of operands, obtain explicitely the leading term of the asymptotic n−1-expansion of the covariance of traces of resolvents of the ensemble and prove the central limit theorem for sufficiently smooth linear eigenvalue statistics as n tends to infinity.