  We prove the Central Limit Theorem for the number of eigenvalues near the
spectrum edge for hermitian ensembles of random matrices. To derive our
results, we use a general theorem, essentially due to Costin and Lebowitz,
concerning the Gaussian fluctuation of the number of particles in random point
fields with determinantal correlation functions. As another corollary of
Costin-Lebowitz Theorem we prove CLT for the empirical distribution function of
the eigenvalues of random matrices from classical compact groups.
