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Universality Limits for Exponential Weights

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Abstract

We establish universality in the bulk for fixed exponential weights on the whole real line. Our methods involve first-order asymptotics for orthogonal polynomials and localization techniques. In particular, we allow exponential weights such as | x | 2β g 2(x)exp (−2Q(x)), where β>−1/2, Q is convex and Q ′′ satisfies some regularity conditions, while g is positive, and has a uniformly continuous and slowly growing or decaying logarithm.

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Authors and Affiliations

  1. Mathematics Department, The Open University of Israel, P.O. Box 808, Raanana, 43107, Israel

    Eli Levin

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Doron S. Lubinsky

Authors
  1. Eli Levin
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  2. Doron S. Lubinsky
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Correspondence to Doron S. Lubinsky.

Additional information

Communicated by Percy A. Deift.

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Levin, E., Lubinsky, D.S. Universality Limits for Exponential Weights. Constr Approx 29, 247–275 (2009). https://doi.org/10.1007/s00365-008-9020-4

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  • DOI: https://doi.org/10.1007/s00365-008-9020-4

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