A New Approach to Universality at the Edge of the Spectrum

We show how localization and smoothing techniques can be used to establish universality at the edge of the spectrum for a fixed positive measure on [-1,1]. Assume that the measure is a regular measure, and is absolutely continuous in some closed neighborhood J of 1. Assume that in J, w = h * Jacobi, where h(1)>0 and h is continuous at 1. Then universality at 1 for ourgiven measure follows from universality at 1 for the classical Jacobi weight. Note that no smoothness is required of h, only continuity.