# Asymptotic Analysis for Extreme Eigenvalues of Principal Minors of Random Matrices

## TL;DR

This paper analyzes the asymptotic behavior of extreme eigenvalues of principal minors of Wishart and Wigner matrices, with applications to high-dimensional statistics, signal processing, and compressed sensing.

## Contribution

It provides new asymptotic results for extreme eigenvalues of principal minors in large random matrices, extending to Wishart and Wigner types, with practical applications.

## Key findings

- Asymptotic distributions of maximum and minimum eigenvalues derived
- Results applicable to high-dimensional statistics and signal processing
- Insights into constructing compressed sensing matrices

## Abstract

Consider a standard white Wishart matrix with parameters $n$ and $p$. Motivated by applications in high-dimensional statistics and signal processing, we perform asymptotic analysis on the maxima and minima of the eigenvalues of all the $m \times m$ principal minors, under the asymptotic regime that $n,p,m$ go to infinity. Asymptotic results concerning extreme eigenvalues of principal minors of real Wigner matrices are also obtained. In addition, we discuss an application of the theoretical results to the construction of compressed sensing matrices, which provides insights to compressed sensing in signal processing and high dimensional linear regression in statistics.