Variance of real zeros of random orthogonal polynomials

2021/01/17 by D. S. Lubinsky, Lubinsky, Doron S., Igor E. Pritsker +1
Mathematics · #30B20 #30C15 #60B10 #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Geometry and complex manifolds #Mathematical functions and polynomials #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2101.06727

openalex publication_date 2021/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

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.

Citations

• On the Variance of the Number of Real Roots of Random Polynomials
• Extremal polynomials associated with a system of curves in the complex plane

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