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We show how localization and smoothing techniques can be used to establish universality in the bulk of the spectrum for a fixed positive measure on OE 1; 1. Assume that is a regular measure, and is absolutely continuous in an open interval containing some point x. Assume moreover, that 0 is positive and continuous at x. Then universality for 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 L p sense under weaker assumptions on :

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Abstract. We present a new method for establishing universality limits in the bulk, based on the theory of entire functions of exponential type. Let be a measure on a compact subset of the real line. Assume that is absolutely continuous in a neighborhood of some point x in the support, and that 0 is bounded above and below near x, which is assumed to be a Lebesgue point of 0 . Then universality holds at x i¤ it holds "along the diagonal", that is lim n!1 Kn x + a n ; x + a n Kn (x; x) = 1;for all real a. The method does not require regularity of the measure as did earlier methods. Moreover, the assumption on the diagonal is certainly satis…ed in the case of regular measures, so that we obtain another proof of some recent results of Simon and Totik.

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