We describe generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite n, which will be expressed through a hypergeometric function. When the dimensional of the Hermitian matrix begins large enough, we will prove that the statistical density of eigenvalues converges in the tight topology to some probability measure, which generalizes the Wigner semi-circle law.

random matrix theory, probability measures, orthogonal polynomials.