Large deviations for the smallest eigenvalue of a deformed GOE with an outlier

TL;DR

This paper proves a large deviation principle for the smallest eigenvalue of a matrix formed by adding a GOE matrix and a diagonal outlier, extending previous results in the field.

Contribution

It generalizes and unifies existing large deviation results for the smallest eigenvalue in deformed GOE models with outliers.

Findings

Established a large deviation principle for the smallest eigenvalue.

Unified previous separate cases into a general framework.

Extended the understanding of eigenvalue fluctuations in deformed random matrices.

Abstract

We establish a large deviation principle for the smallest eigenvalue of a random matrix model composed of the sum of a GOE matrix and a diagonal matrix with an outlier. Our result generalizes and unifies previously studied cases.