Zeros of a random analytic function approach perfect spacing under repeated differentiation

DOI10.1090/tran/6929zbMath1380.30002arXiv1409.7956OpenAlexW2962975523MaRDI QIDQ5367099

Sneha Dey Subramanian, Robin Pemantle

Publication date: 12 October 2017

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.7956

zbMATH Keywords

latticeCauchy integralsaddle pointPoissonrandom seriescoefficienttranslation-invariant

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random power series in one complex variable (30B20)

Related Items (5)

The flow of polynomial roots under differentiation ⋮ Free Convolution Powers Via Roots of Polynomials ⋮ Zeros of derivatives of Gaussian random polynomials on plane domains ⋮ A nonlocal transport equation modeling complex roots of polynomials under differentiation ⋮ Jensen polynomials are not a plausible route to proving the Riemann hypothesis

Cites Work

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• Asymptotic behaviour of symmetric polynomial statistics
• Zeros of derivatives of Riemann's xi-function on the critical line
• The limit behavior of elementary symmetric polynomials of i. i. d. random variables when their order tends to infinity
• Complex zero decreasing sequences
• Negative dependence and the geometry of polynomials
• Unimodal, log-concave and Pólya frequency sequences in combinatorics
• Differentiation evens out zero spacings
• Hyperbolicity and stable polynomials in combinatorics and probability
• Probability
• Zeros of the derivatives of the Riemann zeta-function

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