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The purpose of this note is to establish a Central Limit Theorem for thenumber of eigenvalues of a Wigner matrix in an interval. The proof relies onthe correct aymptotics of the variance of the eigenvalue counting function ofGUE matrices due to Gustavsson, and its extension to large families of Wignermatrices by means of the Tao and Vu Four Moment Theorem and recent localizationresults by Erd\"os, Yau and Yin.

A Note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner Matrices