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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 3, Pages 549–555 (Mi tvp94)  

This article is cited in 4 scientific papers (total in 4 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

Abstract: This paper constructs an example of random polynomials of order $n=1,2,…$ with independent identically distributed coefficients whose average number of real zeros is less than nine for all $n$. The average number $n/2+o(1)$ of complex zeros is concentrated near zero and the same number goes to infinity as $n\to\infty$.

Keywords: random polynomials, average number of real zeros.

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

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English version:
Theory of Probability and its Applications, 2006, 50:3, 529–535

Bibliographic databases:

Received: 12.04.2005

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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\jour Theory Probab. Appl.
\yr 2006
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Theory Probab. Appl., 55:1 (2011), 173–181  mathnet  crossref  crossref  mathscinet  isi
    3. Theory Probab. Appl., 56:4 (2011), 696–703  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. Kabluchko Z. Zaporozhets D., “Roots of Random Polynomials Whose Coefficients Have Logarithmic Tails”, Ann. Probab., 41:5 (2013), 3542–3581  crossref  mathscinet  zmath  isi  elib  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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