Universality at the Edge for Unitary Matrix Models

Journal of Mathematical Physics, Analysis, Geometry: 2012, v.8, No. 4, p. 367-392 Using the results on the $1/n$-expansion of the Verblunsky coefficients for a class of polynomials orthogonal on the unit circle with $n$ varying weight, we prove that the local eigenvalue statistic for unitary matrix models is independent of the form of the potential, determining the matrix model. Our proof is applicable to the case of four times differentiable potentials and of supports, consisting of one interval.