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Article type: Research Article
Authors: Kösters, H.
Affiliations: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany. E-mail: [email protected]
Abstract: 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.
Keywords: random matrix, characteristic polynomial, Airy function, integral representation
DOI: 10.3233/ASY-2010-1004
Journal: Asymptotic Analysis, vol. 69, no. 3-4, pp. 233-248, 2010
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