Large deviations for spectral measures of some spiked matrices

TL;DR

This paper establishes large deviations principles for spectral measures of spiked matrix models, providing two approaches and extending previous work on unperturbed models to understand the impact of perturbations.

Contribution

It introduces two methods to analyze large deviations in spectral measures of perturbed matrices, building on prior results for unperturbed models.

Findings

Large deviations principles are proven for spectral measures of spiked matrices.

Two different analytical approaches are developed for the models.

The work extends previous large deviations results to perturbed matrix settings.

Abstract

We prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large deviations principle of unperturbed models derived in the previous work "Sum rules via large deviations" (Gamboa-Nagel-Rouault, JFA, 2016).