Universality of Poisson Limits for Moduli of Roots of Kac Polynomials-Reference-Cited by-同舟云学术

Universality of Poisson Limits for Moduli of Roots of Kac Polynomials

Published:2022-03-14 Issue:8 Volume:2023 Page:6648-6690
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Cook Nicholas A¹,Nguyen Hoi H²,Yakir Oren³,Zeitouni Ofer⁴

Affiliation:

1. Duke University , Durham, NC 27708, USA

2. Department of Mathematics , The Ohio State University, 231 W 18th Ave., Columbus, OH 43210, USA

3. School of Mathematics , Tel Aviv University, Tel Aviv 6997801, Israel

4. Department of Mathematics , Weizmann Institute of Science, Rehovot 76100, Israel

Abstract

Abstract We give a new proof of a recent resolution [18] by Michelen and Sahasrabudhe of a conjecture of Shepp and Vanderbei [19] 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 from [18] that the Poisson statistics are in fact universal.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2023/8/6648/49863381/rnac021.pdf

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