We obtain large $n$ asymptotics for products of powers of the absolute values of the characteristic polynomials in the Gaussian unitary ensemble (GUE) of ( $n\times n$ )-matrices. Our results can also be interpreted as asymptotics of the determinant of a Hankel matrix whose symbol is supported on the real line and possesses power-like (Fisher-Hartwig) singularities
Publié le : 2007-09-15
Classification:
15A52,
35Q15,
41A60,
47B35
@article{1187916271,
author = {Krasovsky, I. V.},
title = {Correlations of the characteristic polynomials in the Gaussian unitary ensemble or a singular Hankel determinant},
journal = {Duke Math. J.},
volume = {136},
number = {1},
year = {2007},
pages = { 581-619},
language = {en},
url = {http://dml.mathdoc.fr/item/1187916271}
}
Krasovsky, I. V. Correlations of the characteristic polynomials in the Gaussian unitary ensemble or a singular Hankel determinant. Duke Math. J., Tome 136 (2007) no. 1, pp. 581-619. http://gdmltest.u-ga.fr/item/1187916271/