Variance of real zeros of random orthogonal polynomials

Doron S. Lubinsky; Igor E. Pritsker

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arXiv · 2101.06727

Variance of real zeros of random orthogonal polynomials

Doron S. Lubinsky·Igor E. Pritsker

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Abstract

We determine the asymptotics for the variance of the number of zeros of random linear combinations of orthogonal polynomials of degree $\leq n$ in subintervals $\left [ a,b\right ] $ of the support of the underlying orthogonality measure $\mu $. We show that, as $n\rightarrow \infty $, this variance is asymptotic to $cn$, for some explicit constant $c>0$.

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Doron S. Lubinsky, Igor E. Pritsker. 2021-01-17. Variance of real zeros of random orthogonal polynomials. https://arxiv.org/abs/2101.06727

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