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 $\leq n$ in subintervals $\left [ a,b\right ]$ of the support of the underlying orthogonality measure $μ$. We show that, as $n\rightarrow \infty$, this variance is asymptotic to $cn$, for some explicit constant $c>0$.

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