On the number of real roots of random polynomials

Hoi Nguyen, Oanh Nguyen, Van Vu

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

Roots of random polynomials have been studied intensively in both analysis and probability for a long time. A famous result by Ibragimov and Maslova, generalizing earlier fundamental works of Kac and Erdos-Offord, showed that the expectation of the number of real roots is 2/π log n + o(log n). In this paper, we determine the true nature of the error term by showing that the expectation equals 2/π log n + O(1). Prior to this paper, the error term O(1) has been known only for polynomials with Gaussian coefficients.

Original languageEnglish (US)
Article number1550052
JournalCommunications in Contemporary Mathematics
Volume18
Issue number4
DOIs
StatePublished - Aug 1 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Number of real roots
  • Random polynomials
  • Roots repulsion

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