# A new approach to universality limits involving orthogonal polynomials | Annals of Mathematics

Abstract We show how localization and smoothing techniques can be used to establish universality in the bulk of the spectrum for a fixed positive measure μ on [−1,1]. Assume that μ is a regular measure, and is absolutely continuous in an open interval containing some point x. Assume moreover, that μ′ is positive and continuous at x. Then universality for μ holds at x. If the hypothesis holds for x in a compact subset of (−1,1), universality holds uniformly for such x. Indeed, this follows from universality for the classical Legendre weight. We also establish universality in an Lp sense under weaker assumptions on μ.

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### 数学年刊（Annals of Mathematics）

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