Asymptotics of Characteristic Polynomials of Wigner Matrices at the Edge of the Spectrum
Abstract
Description
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.
15 pages; minor changes
15 pages; minor changes