# Spectral Measures of Spiked Random Matrices

## TL;DR

This paper investigates spectral properties of spiked random matrices, providing new insights into eigenvector behavior under additive and multiplicative perturbations in high-dimensional settings.

## Contribution

It introduces a unified framework for analyzing spectral measures of spiked models, extending classical results to more general perturbations.

## Key findings

- Characterization of eigenvector coordinates in spiked models
- Extension of spectral measure analysis to additive and multiplicative cases
- New results on eigenvector localization and spectral distribution

## Abstract

We study two spiked models of random matrices under general frameworks corresponding respectively to additive deformation of random symmetric matrices and multiplicative perturbation of random covariance matrices. In both cases, the limiting spectral measure in the direction of an eigenvector of the perturbation leads to old and new results on the coordinates of eigenvectors.