Central limit theorem for moments of spectral measures of Wigner matrices

TL;DR

This paper proves the Wigner semicircle law and establishes a central limit theorem for the moments of spectral measures of Wigner matrices, using combinatorial and moment methods.

Contribution

It introduces a CLT for spectral measure moments of Wigner matrices, extending the understanding of their probabilistic behavior.

Findings

Proves the Wigner semicircle law for spectral measures.

Derives a central limit theorem for spectral measure moments.

Uses combinatorial and moment methods in the proof.

Abstract

Spectral measures of Wigner matrices are investigated. The Wigner semicircle law for spectral measures is proved. Regard this as the law of large number, the central limit theorem for moments spectral measure is also derived. The proof is based on moment method and combinatorial method.