Subramanian, Sneha Dey On the distribution of critical points of a polynomial. (English) Zbl 1261.60051 Electron. Commun. Probab. 17, Paper No. 37, 9 p. (2012). Summary: This paper proves that, for points \(Z_1,Z_2,\dots\) independently and identically chosen using some measure \(\mu\) from the unit circle in the complex plane, with \(p_n(z) = (z-Z_1)(z-Z_2)\dotsm(z-Z_n)\), the empirical distribution of the critical points of \(p_n\) converges weakly to \(\mu\). Cited in 18 Documents MSC: 60G99 Stochastic processes Keywords:critical points; random polynomials; Pemantle-Rivin conjecture × Cite Format Result Cite Review PDF Full Text: DOI arXiv