Distances between zeroes and critical points for random polynomials with i.i.d. zeroes

@article{Kabluchko2018DistancesBZ,
  title={Distances between zeroes and critical points for random polynomials with i.i.d. zeroes},
  author={Zakhar Kabluchko and Hauke Seidel},
  journal={Electronic Journal of Probability},
  year={2018},
  volume={24}
}
  • Zakhar Kabluchko, Hauke Seidel
  • Published 2018
  • Mathematics
  • Electronic Journal of Probability
  • Consider a random polynomial $Q_n$ of degree $n+1$ whose zeroes are i.i.d. random variables $\xi_0,\xi_1,\ldots,\xi_n$ in the complex plane. We study the pairing between the zeroes of $Q_n$ and its critical points, i.e. the zeroes of its derivative $Q_n'$. In the asymptotic regime when $n\to\infty$, with high probability there is a critical point of $Q_n$ which is very close to $\xi_0$. We localize the position of this critical point by proving that the difference between $\xi_0$ and the… CONTINUE READING

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