On the number of real roots of random polynomials

Hoi Nguyen, Oanh Nguyen, Van Vu

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


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
Issue number4
StatePublished - Aug 1 2016

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Number of real roots
  • Random polynomials
  • Roots repulsion


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