Bulk Universality for Unitary Matrix Models - Poplavskyi, M. (Журнал математичної фізики, аналізу, геометрії, 2009)
A proof of universality in the bulk of spectrum of unitary matrix models, assuming that the potential is globally $C^2$ and locally $C^3$ function (see Theorem 1.2), is given. The proof is based on the determinant formulas for correlation functions in terms of polynomials orthogonal on the unit circle. The $sin$-kernel is obtained as a unique solution of a certain nonlinear integro-differential equation without using asymptotics of orthogonal polynomials. Mathematics Subject Classification: 15A52, 15A57.