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Universality of Poisson limits for moduli of roots of Kac polynomials

Publication ,  Journal Article
Cook, NA; Nguyen, HH; Yakir, O; Zeitouni, O
May 18, 2021

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.

Duke Scholars

Publication Date

May 18, 2021
 

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Cook, N. A., Nguyen, H. H., Yakir, O., & Zeitouni, O. (2021). Universality of Poisson limits for moduli of roots of Kac polynomials.
Cook, Nicholas A., Hoi H. Nguyen, Oren Yakir, and Ofer Zeitouni. “Universality of Poisson limits for moduli of roots of Kac polynomials,” May 18, 2021.
Cook NA, Nguyen HH, Yakir O, Zeitouni O. Universality of Poisson limits for moduli of roots of Kac polynomials. 2021 May 18;
Cook NA, Nguyen HH, Yakir O, Zeitouni O. Universality of Poisson limits for moduli of roots of Kac polynomials. 2021 May 18;

Publication Date

May 18, 2021