D. N. Zaporozhets, “An example of a random polynomial with unusual behavior of roots”, Teor. Veroyatnost. i Primenen., 50:3 (2005), 549–555; Theory Probab. Appl., 50:3 (2006), 529

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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 3, Pages 549–555
DOI: https://doi.org/10.4213/tvp94 (Mi tvp94)

This article is cited in 6 scientific papers (total in 6 papers)

Short Communications

An example of a random polynomial with unusual behavior of roots

D. N. Zaporozhets

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Full-text PDF (649 kB) Citations (6)

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DOI: https://doi.org/10.4213/tvp94

Abstract: This paper constructs an example of random polynomials of order

n = 1, 2, \dots

$n=1,2,\dots$ with independent identically distributed coefficients whose average number of real zeros is less than nine for all

n

$n$ . The average number

n / 2 + o (1)

$n/2+o(1)$ of complex zeros is concentrated near zero and the same number goes to infinity as

n \to \infty

$n\to\infty$ .

Keywords: random polynomials, average number of real zeros.

Received: 12.04.2005

English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 3, Pages 529–535
DOI: https://doi.org/10.1137/S0040585X97981871

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: D. N. Zaporozhets, “An example of a random polynomial with unusual behavior of roots”, Teor. Veroyatnost. i Primenen., 50:3 (2005), 549–555; Theory Probab. Appl., 50:3 (2006), 529–535

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tvp94

https://doi.org/10.4213/tvp94

https://www.mathnet.ru/eng/tvp/v50/i3/p549

This publication is cited in the following 6 articles:

Ken Söze, “Real zeroes of random polynomials, I. Flip-invariance, Turán's lemma, and the Newton-Hadamard polygon”, Isr. J. Math., 220:2 (2017), 817
Kabluchko Z. Zaporozhets D., “Roots of Random Polynomials Whose Coefficients Have Logarithmic Tails”, Ann. Probab., 41:5 (2013), 3542–3581
Ildar Ibragimov, Dmitry Zaporozhets, Springer Proceedings in Mathematics & Statistics, 33, Prokhorov and Contemporary Probability Theory, 2013, 303
Theory Probab. Appl., 56:4 (2011), 696–703
Theory Probab. Appl., 55:1 (2011), 173–181
D. N. Zaporozhets, A. I. Nazarov, “What is the Least Expected Number of Real Roots of a Random Polynomial?”, Theory Probab. Appl., 53:1 (2009), 117–133

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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