Fine Structure of the Zeros of Orthogonal Polynomials, I. A Tale of Two Pictures

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Mhaskar-Saff found a kind of universal behavior for the bulk structure of the zeros of orthogonal polynomials for large n. Motivated by two plots, we look at the finer structure for the case of random Verblunsky coefficients and for what we call the BLS condition: αₙ = Cbⁿ + O((bΔ)ⁿ). In the former case, we describe results of Stoiciu. In the latter case, we prove asymptotically equal spacing for the bulk of zeros.