On the Distribution of Critical Points of a Polynomial

2012/06/30 by Sneha Dey Subramanian, Subramanian, Sneha Dey
Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1207.0125

openalex publication_date 2012/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper proves that if points Z₁,Z₂,... are chosen independently and identically using some measure μ from the unit circle in the complex plane, with p_n(z) = (z-Z₁)(z-Z₂)...(z-Z_n), then the empirical distribution of the critical points of p_n converges weakly to μ.

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