Roots of random polynomials with coefficients of polynomial growth

Yen Do, Oanh Nguyen, Van Vu

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


In this paper, we prove optimal local universality for roots of random polynomials with arbitrary coefficients of polynomial growth. As an application, we derive, for the first time, sharp estimates for the number of real roots of these polynomials, even when the coefficients are not explicit. Our results also hold for series; in particular, we prove local universality for random hyperbolic series.

Original languageEnglish (US)
Pages (from-to)2407-2494
Number of pages88
JournalAnnals of Probability
Issue number5
StatePublished - Sep 1 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Arbitrary coefficients
  • Complex roots
  • Correlation
  • Random polynomials
  • Real roots
  • Universality


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