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On the distribution of critical points of a polynomial. (English) Zbl 1261.60051

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 \(\mu\).

MSC:

60G99 Stochastic processes