On the correlation function of the characteristic polynomials of the hermitian Wigner ensemble

Abstract

We consider the asymptotics of the correlation functions of the characteristic polynomials of the hermitian Wigner matrices $H_n=n^{-1/2}{W}_n$. We show that for the correlation function of any even order the asymptotic coincides with this for the GUE up to a factor, depending only on the forth moment of the common probability law $Q$ of entries $\Im W_{jk}$, $\Re W_{jk}$, i.e. that the higher moments of $Q$ do not contribute to the above limit.

20 p

References in corpus (3)

• Characteristic polynomials of real symmetric random matrices
• Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach
• On the Second-Order Correlation Function of the Characteristic Polynomial of a Hermitian Wigner Matrix

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• Characteristic polynomials for random band matrices near the threshold
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• Characteristic polynomials of products of Wigner matrices: finite-N results and Lyapunov universality