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On the distribution of critical points of a polynomial

   
@article{ECP2040,
	author = {Sneha Subramanian},
	title = {On the distribution of critical points of a polynomial},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {17},
	year = {2012},
	keywords = {critical points; random polynomials; Pemantle-Rivin conjecture},
	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 $\mu$.
},
	pages = {no. 37, 1-9},
	issn = {1083-589X},
	doi = {10.1214/ECP.v17-2040},    
        url = {http://ecp.ejpecp.org/article/view/2040}}