The spectrum of large unitarily invariant models with increasingly many spikes

In this paper we study random matrix models where the matrices in question contain infinitely many spikes. Recent work has characterized the possible outliers in the spectrum of large deformed unitarily invariant models when the number of spikes in the model is fixed. We show that similar results hold when the number of spikes grows along with the size of the matrix and these spikes accumulate to the support of the limiting eigenvalue distribution.