On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix

Abstract

We consider the asymptotics of the second-order correlation function of the characteristic polynomial of a random matrix. We show that the known result for a random matrix from the Gaussian Unitary Ensemble essentially continues to hold for a general Hermitian Wigner matrix. Our proofs rely on an explicit formula for the exponential generating function of the second-order correlation function of the characteristic polynomial.

20 pages

References in corpus (4)

• Characteristic polynomials of random matrices
• Products and Ratios of Characteristic Polynomials of Random Hermitian Matrices
• Characteristic polynomials of real symmetric random matrices
• Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach

Cited by in corpus (4)

• On the correlation function of the characteristic polynomials of the hermitian Wigner ensemble
• On the correlation functions of the characteristic polynomials of the sparse hermitian random matrices
• Characteristic polynomials for random band matrices near the threshold
• Characteristic polynomials of products of Wigner matrices: finite-N results and Lyapunov universality