A New Approach to Universality Limits involving Orthogonal Polynomials

Details A New Approach to Universality Limits involving Orthogonal Polynomials A New Approach to Universality Limits involving Orthogonal Polynomials

2007-01-10

arxiv.org/abs/math/0701307v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We show how localization and smoothing techniques can be used to establish universality in the bulk of the spectrum for a fixed positive measure mu on [-1,1]. Assume that mu is a regular measure, and is absolutely continuous in an open interval containing some closed subinterval J of (-1,1). Assume that in J, the absolutely continuous component mu' is positive and continuous. Then universality in J for mu follows from universality for the classical Legendre weight. We also establish universality in an L_{p} sense under weaker assumptions on mu.

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