Variance of real zeros of random orthogonal polynomials

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 μ. We show that, as n→∞, this variance is asymptotic to cn, for some explicit constan...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 498; no. 1; p. 124954
Main Authors Lubinsky, Doron S., Pritsker, Igor E.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2021
Subjects
Orthogonal polynomials
Random polynomials
Real zeros
Variance
Real zeros
Random polynomials
Variance
Orthogonal polynomials
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Summary: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 μ. We show that, as n→∞, this variance is asymptotic to cn, for some explicit constant c>0.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.124954