Universality of Poisson limits for moduli of roots of Kac polynomials

Nicholas A. Cook; Hoi H. Nguyen; Oren Yakir; Ofer Zeitouni

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arXiv · 2105.08592

Universality of Poisson limits for moduli of roots of Kac polynomials

Nicholas A. Cook·Hoi H. Nguyen·Oren Yakir·Ofer Zeitouni

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Abstract

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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Nicholas A. Cook, Hoi H. Nguyen, Oren Yakir, Ofer Zeitouni. 2021-05-18. Universality of Poisson limits for moduli of roots of Kac polynomials. https://arxiv.org/abs/2105.08592

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