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In this paper we characterize the possible outliers in the spectrum of largedeformed unitarily invariant additive and multiplicative models, as well as theeigenvectors corresponding to them. We allow both the non-deformed unitarilyinvariant model and the perturbation matrix to have non-trivial limitingspectral measures and spiked outliers in their spectrum. We uncover aremarkable new phenomenon: a single spike can generate asymptotically severaloutliers in the spectrum of the deformed model. The free subordinationfunctions play a key role in this analysis.

Outliers in the spectrum of large deformed unitarily invariant models