On the Distribution of Critical Points of a Polynomial

Sneha Dey Subramanian

On the Distribution of Critical Points of a Polynomial

Probability 2012-10-22 v2

Authors: Sneha Dey Subramanian

Abstract

This paper proves that if points $Z_1,Z_2,...$ are chosen independently and identically using some measure $\mu$ from the unit circle in the complex plane, with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$ , then the empirical distribution of the critical points of $p_n$ converges weakly to $\mu$ .

Keywords

critical points polynomials empirical distribution weak convergence random zeros

Cite

@article{arxiv.1207.0125,
  title  = {On the Distribution of Critical Points of a Polynomial},
  author = {Sneha Dey Subramanian},
  journal= {arXiv preprint arXiv:1207.0125},
  year   = {2012}
}

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