Mesoscopic eigenvalue statistics of Wigner matrices

Abstract

We prove that the linear statistics of the eigenvalues of a Wigner matrix converge to a universal Gaussian process on all mesoscopic spectral scales, i.e. scales larger than the typical eigenvalue spacing and smaller than the global extent of the spectrum.

34 pages

References in corpus (3)

• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• Lectures on the local semicircle law for Wigner matrices
• Mesoscopic linear statistics of Wigner matrices

Cited by in corpus (1)

• Isotropic self-consistent equations for mean-field random matrices