Equidistribution of zeros of random polynomials

@article{Pritsker2017EquidistributionOZ,
  title={Equidistribution of zeros of random polynomials},
  author={I. Pritsker and K. Ramachandran},
  journal={J. Approx. Theory},
  year={2017},
  volume={215},
  pages={106-117}
}
  • I. Pritsker, K. Ramachandran
  • Published 2017
  • Mathematics, Computer Science
  • J. Approx. Theory
  • We study the asymptotic distribution of zeros for the random polynomials $P_n(z) = \sum_{k=0}^n A_k B_k(z)$, where $\{A_k\}_{k=0}^{\infty}$ are non-trivial i.i.d. complex random variables. Polynomials $\{B_k\}_{k=0}^{\infty}$ are deterministic, and are selected from a standard basis such as Szeg\H{o}, Bergman, or Faber polynomials associated with a Jordan domain $G$ bounded by an analytic curve. We show that the zero counting measures of $P_n$ converge almost surely to the equilibrium measure… CONTINUE READING
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