We characterize the possible outliers in the spectrum of large deformed unitarily invariant additive and multiplicative models, as well as the eigenvectors corresponding to them. We allow both the nondeformed unitarily invariant model and the perturbation matrix to have nontrivial limiting eigenvalue distributions and spiked outliers in their spectrum. The free subordination functions play a key role in this analysis.
"Outliers in the spectrum of large deformed unitarily invariant models." Ann. Probab. 45 (6A) 3571 - 3625, November 2017. https://doi.org/10.1214/16-AOP1144