On the distribution of critical points of a polynomial

Sneha Dey Subramanian (University of Pennsylvania)

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 $\mu$.


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Pages: 1-9

Publication Date: August 26, 2012

DOI: 10.1214/ECP.v17-2040

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