期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2013
卷号：X
页码：27-44
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We establish a moderate deviation principle (MDP) for the number ofeigenvalues of aWigner matrix in an interval. The proof relies on fine asymptotics ofthe variance of the eigenvalue counting function of GUE matrices due to Gustavsson.The extension to certain families of Wigner matrices is based on the Tao and VuFour Moment Theorem and applies localization results by Erd¨os, Yau and Yin.Moreover we investigate families of covariance matrices as well.
关键词：Large deviations; moderate deviations; Wigner random matrices; co-;variance matrices; Gaussian ensembles; four moment theorem.
