## Asymptotic behavior of the Verblunsky coefficients for the OPUC with a varying weight    [PDF]

Poplavskyi Mihail
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.
View original: http://arxiv.org/abs/1006.5515