Journal article
Asymptotic corrections to the eigenvalue density of the GUE and LUE
TM Garoni, PJ Forrester, NE Frankel
JOURNAL OF MATHEMATICAL PHYSICS | AMER INST PHYSICS | Published : 2005
DOI: 10.1063/1.2035028
Abstract
We obtain correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N×N matrices, both in the bulk of the spectrum and near the spectral edge. This is achieved by using the well known orthogonal polynomial expression for the kernel to construct a double contour integral representation for the density, to which we apply the saddle point method. The main correction to the bulk density is oscillatory in N and depends on the distribution function of the limiting density, while the corrections to the Airy kernel at the soft edge are again expressed in terms of the Airy function and its first derivative. We dem..
View full abstract