Non-Gaussian Limiting Laws for the Entries of Regular Functions of the Wigner Matrices

Abstract

This paper is a continuation of our paper "Fluctuations of Matrix Elements of Regular Functions of Gaussian Random Matrices", J. Stat. Phys. (134), 147--159 (2009), in which we proved the Central Limit Theorem for the matrix elements of differential functions of the real symmetric random Gaussian matrices (GOE). Here we consider the real symmetric random Wigner matrices having independent (modulo symmetry conditions) but not necessarily Gaussian entries. We show that in this case the matrix elements of sufficiently smooth functions of these random matrices have in general another limiting law which coincides essentially with the probability law of matrix entries.

References in corpus (2)

• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• On Asymptotic Properties of Large Random Matrices with Independent Entries

Cited by in corpus (5)

• Fluctuations of interlacing sequences
• On Non-Gaussian Limiting Laws for the Certain Statistics of the Wigner Matrices
• On Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices with Non-Identically Distributed Entries
• The Common Limit of the Linear Statistics of Zeros of Random Polynomials and Their Derivatives
• On Finite Rank Deformations of Wigner Matrices II: Delocalized Perturbations