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

作者：Liu Dang Zheng^*; Wang Zheng Dong; Yan Kui Hua

来源：Journal of Approximation Theory, 2010, 162(9): 1588-1606.

DOI：10.1016/j.jat.2010.04.005

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. By using a new method, we calculate directly the moments of the density (which has been obtained in the work of Nevai and Dehesa, Van Assche and others on asymptotic zero distribution), and prove that scaling eigenvalues converge weakly, in probability and almost surely to the Nevai-Ullmann measure. Furthermore, we can prove that the density is invariant when the weight function is perturbed by a polynomial.

• 出版日期2010-9
• 单位北京大学