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