Density of eigenvalues and its perturbation invariance in unitary ensembles of random matrices

We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density. Then, by studying some deformation of the moments, we get a family of differential equations of first order which the densities satisfy

• Type: Journal
• Year: 2010
• Where: JAT
• Authors: Dang-Zheng Liu, Zheng-Dong Wang, Kui-Hua Yan
• Keywords: JAT 2010, Orthogonal Polynomials, Random Matrices, Unitary Ensembles