# The spectrum of large unitarily invariant models with increasingly many spikes

## TL;DR

This paper extends the understanding of large unitarily invariant random matrix models by analyzing the spectral behavior when the number of spikes increases with matrix size, revealing that outlier phenomena persist under these conditions.

## Contribution

It demonstrates that spectral outlier results for fixed spikes also apply when spikes grow with matrix size and accumulate to the eigenvalue distribution support.

## Key findings

- Outliers exist when spikes grow with matrix size.
- Spikes can accumulate to the eigenvalue support.
- Results generalize previous fixed-spike models.

## Abstract

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.