Variance of real zeros of random orthogonal polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:498

Article

Lubinsky, Doron S.¹  Pritsker, Igor E.² 

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA

关键词: Random polynomials;    Real zeros;    Variance;    Orthogonal polynomials;   

DOI  :  10.1016/j.jmaa.2021.124954

来源: Elsevier

【 摘 要 】

We determine the asymptotics for the variance of the number of zeros of random linear combinations of orthogonal polynomials of degree <= n in subintervals [a, b] of the support of the underlying orthogonality measure mu. We show that, as n -> infinity, this variance is asymptotic to cn, for some explicit constant c > 0. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free