A New Approach to Universality Limits involving Orthogonal Polynomials

2007/01/10 by Doron S Lubinsky, Lubinsky, Doron S · 5 citations
Mathematics · #41 #42 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:41 #msc:42

paper · pdf · doi:10.48550/arxiv.math/0701307

arxiv created 2007/01/10 · arxiv updated 2009/12/01

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.

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