Electronic Communications in Probability

On the distribution of critical points of a polynomial

Sneha Subramanian

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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 $\mu$.

Article information

Source
Electron. Commun. Probab., Volume 17 (2012), paper no. 37, 9 pp.

Dates
Accepted: 26 August 2012
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465263170

Digital Object Identifier
doi:10.1214/ECP.v17-2040

Mathematical Reviews number (MathSciNet)
MR2970701

Zentralblatt MATH identifier
1261.60051

Subjects
Primary: 60G99: None of the above, but in this section

Keywords
critical points random polynomials Pemantle-Rivin conjecture

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Subramanian, Sneha. On the distribution of critical points of a polynomial. Electron. Commun. Probab. 17 (2012), paper no. 37, 9 pp. doi:10.1214/ECP.v17-2040. https://projecteuclid.org/euclid.ecp/1465263170


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