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