Universality of Poisson limits for moduli of roots of Kac polynomials

2021/05/18 by Cook, Nicholas A., Nguyen, Hoi H., Yakir, Oren +1
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2105.08592

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 n², 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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