Asymptotics of Characteristic Polynomials of Wigner Matrices at the Edge of the Spectrum

Details Asymptotics of Characteristic Polynomials of Wigner Matrices at the Edge of the Spectrum Asymptotics of Characteristic Polynomials of Wigner Matrices at the Edge of the Spectrum

2008-05-20

arxiv.org/abs/0805.3044v2

Mathematics

Probability

15 pages; minor changes

Scientific paper

We investigate the asymptotic behaviour of the second-order correlation function of the characteristic polynomial of a Hermitian Wigner matrix at the edge of the spectrum. We show that the suitably rescaled second-order correlation function is asymptotically given by the Airy kernel, thereby generalizing the well-known result for the Gaussian Unitary Ensemble (GUE). Moreover, we obtain similar results for real-symmetric Wigner matrices.

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