For random linear combinations of OPUC in the Nevai class with complex Gaussian coefficients, the variance of the number of zeros in an annulus away from the unit circle converges to an explicit closed-form formula.
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The Variance of the Number of Zeros for Complex Random Polynomials Spanned by OPUC
For random linear combinations of OPUC in the Nevai class with complex Gaussian coefficients, the variance of the number of zeros in an annulus away from the unit circle converges to an explicit closed-form formula.