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 moments of spectral measures is also derived. The proof is based on moment method and combinatorial method.
"Central limit theorem for moments of spectral measures of Wigner matrices." Osaka J. Math. 53 (1) 141 - 161, January 2016.