Asymptotic behavior of the Verblunsky coefficients for the OPUC with a varying weight

Abstract

We present an asymptotic analysis of the Verblunsky coefficients for the polynomials orthogonal on the unit circle with the varying weight $e^{-nV(\cos x)}$, assuming that the potential $V$ has four bounded derivatives on $[-1,1]$ and the equilibrium measure has a one interval support. We obtain the asymptotics as a solution of the system of "string" equations.

28 pages

References in corpus (4)

• Bulk Universality and Related Properties of Hermitian Matrix Models
• Unitary Matrix Models and Painlevé III
• On the edge universality of the local eigenvalue statistics of matrix models
• Bulk Universality for Unitary Matrix Models