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.
On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix
On the Second-Order Correlation Function of the Characteristic Polynomial of a Real Symmetric Wigner Matrix
Characteristic Polynomials of Sample Covariance Matrices: The Non-Square Case
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