Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices

Abstract

We study the fluctuations of the matrix entries of regular functions of Wigner random matrices in the limit when the matrix size goes to infinity. In the case of the Gaussian ensembles (GOE and GUE) this problem was considered by A.Lytova and L.Pastur in J. Stat. Phys., v.134, 147-159 (2009). Our results are valid provided the off-diagonal matrix entries have finite fourth moment, the diagonal matrix entries have finite second moment, and the test functions have four continuous derivatives in a neighborhood of the support of the Wigner semicircle law.

minor corrections; the manuscript will appear in the Journal of Statistical Physics

References in corpus (3)

• Random matrices: Universality of local eigenvalue statistics up to the edge
• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• Central limit theorems for eigenvalues in a spiked population model

Cited by in corpus (3)

• Gaussian fluctuations for linear spectral statistics of large random covariance matrices
• Fluctuations of Linear Eigenvalue Statistics of Random Band Matrices
• Fluctuations of Functions of Wigner Matrices