On the Distribution of Critical Points of a Polynomial

Sneha Dey Subramanian

Published 2012-06-30, updated 2012-10-19Version 2

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 $\mu$.