A New Approach to Universality Limits involving Orthogonal Polynomials
Classical Analysis and ODEs
2007-05-23 v1
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 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.
Cite
@article{arxiv.math/0701307,
title = {A New Approach to Universality Limits involving Orthogonal Polynomials},
author = {Doron S Lubinsky},
journal= {arXiv preprint arXiv:math/0701307},
year = {2007}
}