  We present some applications of central limit theorems on mesoscopic scales
for random matrices. When combined with the recent theory of "homogenization"
for Dyson Brownian Motion, this yields the universality of quantities which
depend on the behavior of single eigenvalues of Wigner matrices and
$\beta$-ensembles. Among the results we obtain are the Gaussian fluctuations of
single eigenvalues for Wigner matrices (without an assumption of 4 matching
moments) and classical $\beta$-ensembles ($\beta=1, 2, 4$), Gaussian
fluctuations of the eigenvalue counting function, and an asymptotic expansion
up to order $o(N^{-1})$ for the expected value of eigenvalues in the bulk of
the spectrum. The latter result solves a conjecture of Tao and Vu.
