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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
Published in: International Mathematics Research Notices
April 1, 2023

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.

Duke Scholars

Published In

International Mathematics Research Notices

DOI

EISSN

1687-0247

ISSN

1073-7928

Publication Date

April 1, 2023

Volume

2023

Issue

8

Start / End Page

6648 / 6690

Related Subject Headings

  • General Mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
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Cook, N. A., Nguyen, H. H., Yakir, O., & Zeitouni, O. (2023). Universality of Poisson Limits for Moduli of Roots of Kac Polynomials. International Mathematics Research Notices, 2023(8), 6648–6690. https://doi.org/10.1093/imrn/rnac021
Cook, N. A., H. H. Nguyen, O. Yakir, and O. Zeitouni. “Universality of Poisson Limits for Moduli of Roots of Kac Polynomials.” International Mathematics Research Notices 2023, no. 8 (April 1, 2023): 6648–90. https://doi.org/10.1093/imrn/rnac021.
Cook NA, Nguyen HH, Yakir O, Zeitouni O. Universality of Poisson Limits for Moduli of Roots of Kac Polynomials. International Mathematics Research Notices. 2023 Apr 1;2023(8):6648–90.
Cook, N. A., et al. “Universality of Poisson Limits for Moduli of Roots of Kac Polynomials.” International Mathematics Research Notices, vol. 2023, no. 8, Apr. 2023, pp. 6648–90. Scopus, doi:10.1093/imrn/rnac021.
Cook NA, Nguyen HH, Yakir O, Zeitouni O. Universality of Poisson Limits for Moduli of Roots of Kac Polynomials. International Mathematics Research Notices. 2023 Apr 1;2023(8):6648–6690.
Journal cover image

Published In

International Mathematics Research Notices

DOI

EISSN

1687-0247

ISSN

1073-7928

Publication Date

April 1, 2023

Volume

2023

Issue

8

Start / End Page

6648 / 6690

Related Subject Headings

  • General Mathematics
  • 0101 Pure Mathematics