Characteristic Polynomials of Sample Covariance Matrices

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.

26 pages

References in corpus (2)

• Random matrices: The distribution of the smallest singular values
• Asymptotics of Characteristic Polynomials of Wigner Matrices at the Edge of the Spectrum