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Universality of Poisson limits for moduli of roots of Kac polynomials
Nicholas A. Cook, Hoi H. Nguyen, Oren Yakir, Ofer Zeitouni · 2021-05-18 · via math.PR updates on arXiv.org

We give a new proof of a recent resolution by Michelen and Sahasrabudhe of a conjecture of Shepp and Vanderbei that the moduli of roots of Gaussian Kac polynomials of degree $n$, centered at $1$ and rescaled by $n^2$, should form a Poisson point process. We use this new approach to verify a conjecture of Michelen and Sahasrabudhe that the Poisson statistics are in fact universal.

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