Abstract
We consider varying weights \( \left\{e^{-2nQ_{n}}\right\}\) and establish bounds and asymptotics for their orthonormal polynomials, and associated quantities, when \( \left\{ Q_{n}\right\}\) are convex and \( \left\{ Q_{n}^{\prime }\right\} \) satisfy a uniform Hölder condition of appropriate order. We deduce universality limits for related unitary ensembles, and asymptotics for entropy integrals.
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Levin, E., Lubinsky, D.S. (2018). Introduction. In: Bounds and Asymptotics for Orthogonal Polynomials for Varying Weights. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-72947-3_1
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DOI: https://doi.org/10.1007/978-3-319-72947-3_1
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