Polynomials orthogonal on the unit circle with n-varying exponential weights

Abstract:
We consider a polynomials orthogonal on the unit circle with exponential n-varying weight. These polynomials play a big role in the studying of universality of the local eigenvalue statistics for unitary matrix models. Assuming that the support of corresponded equilibrium measure is the arc of the unit circle we prove asymptotic relations for the Verblunsky coefficients, analogue for the Jacobi coefficients in the real line case.

Presentation