Characteristic Polynomials of Sample Covariance Matrices

TL;DR

This paper studies the second-order correlation function of the characteristic polynomial of sample covariance matrices, deriving explicit formulas and connecting to known kernels in random matrix theory.

Contribution

It provides explicit formulas for the correlation functions and links them to classical kernels, enhancing understanding of sample covariance matrices.

Findings

Derived explicit formulas for correlation functions

Reproduced well-known kernels from random matrix theory

Connected characteristic polynomial behavior to classical kernels

Abstract

We investigate the second-order correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for the generating function, we re-obtain several well-known kernels from random matrix theory.