Analysis/Mathematical Physics Seminar

We present a new approach to some of the universality limits that arise in orthogonal polynomials. For example, we show that if w is a fixed weight positive a.e. in [-1,1], and w satisfies a Dini condition in some subinterval of (-1,1), then there is the uniform universality limit in that subinterval. If we assume no smoothness, but only that w is bounded below in some subinterval, then the universality limit holds in an L1 sense.