Nevai's condition for measures with unbounded supports

Abstract

We study Nevai's condition from the theory of orthogonal polynomials on the real line. We prove that a large class of measures with unbounded Jacobi parameters satisfies Nevai's condition locally uniformly on the support of the measure away from a finite explicit set. This allows us to give applications to relative uniform and weak asymptotics of Christoffel-Darboux kernels on the diagonal and to limit theorems for unconventionally normalized global linear statistics of orthogonal polynomial ensembles.

20 pages

References in corpus (4)

• Orthogonal polynomial ensembles in probability theory
• Orthogonal polynomials with periodically modulated recurrence coefficients in the Jordan block case II
• An approach to universality using Weyl m-functions
• Asymptotic zeros' distribution of orthogonal polynomials with unbounded recurrence coefficients