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  • The zeros of random polynomials cluster uniformly near the unit circle

  • Part of
  • C. P. Hughes, A. Nikeghbali
  • Journal:
    Compositio Mathematica / Volume 144 / Issue 3 / May 2008
    Published online by Cambridge University Press:
    01 May 2008, pp. 734-746
    Print publication:
    May 2008
    • Article
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  • In this paper we deduce a universal result about the asymptotic distribution of roots of random polynomials, which can be seen as a complement to an old and famous result of Erdős and Turan. More precisely, given a sequence of random polynomials, we show that, under some very general conditions, the roots tend to cluster near the unit circle, and their angles are uniformly distributed. The method we use is deterministic: in particular, we do not assume independence or equidistribution of the coefficients of the polynomial.