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For random polynomials with independent and identically distributed (i.i.d.) zeros following any common probability distribution $$\mu $$ μ with support contained in the unit circle, the empirical measures of the zeros of their first and higher-order derivatives will be proved to converge weakly to $$\mu $$ μ almost surely (a.s.). This, in particular, completes a recent work of Subramanian on the first-order derivative case where $$\mu $$ μ was assumed to be non-uniform. The same almost sure weak convergence will also be shown for polar and Sz.-Nagy’s generalized derivatives, assuming some mild conditions.
Computational Methods and Function Theory – Springer Journals
Published: Jan 21, 2015
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