  Basing on our recent results on the $1/n$-expansion in unitary invariant
random matrix ensembles, known as matrix models, we prove that the local
eigenvalue statistic, arising in a certain neighborhood of the edges of the
support of the Density of States, is independent of the form of the potential,
determining the matrix model. Our proof is applicable to the case of real
analytic potentials and of supports, consisting of one or two disjoint
intervals.
