2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58359We 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.The essential alterations are a slightly different formulation of the Costin-Lebowitz Theorem and the addition of Remark 4 in the section 2Mathematical PhysicsProbabilitytext