Moderate deviations for the eigenvalue counting function of Wigner matrices

Abstract

We establish a moderate deviation principle (MDP) for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on fine asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson. The extension to large families of Wigner matrices is based on the Tao and Vu Four Moment Theorem and applies localization results by Erdös, Yau and Yin. Moreover we investigate families of covariance matrices as well.

20 pages

References in corpus (3)

• Random matrices: Universality of local eigenvalue statistics up to the edge
• Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices
• Functional moderate deviations for triangular arrays and applications

Cited by in corpus (5)

• Random matrices: The Four Moment Theorem for Wigner ensembles
• Precise Deviations Results for the Maxima of Some Determinantal Point Processes: the Upper Tail
• Moderate deviations for spectral measures of random matrix ensembles
• Tridiagonal random matrix: Gaussian fluctuations and deviations
• Gaussian fluctuations and moderate deviations of eigenvalues in unitary invariant ensembles