Limiting empirical distribution of zeros and critical points of random polynomials agree in general

DOI10.1214/17-EJP85zbMath1376.30003arXiv1609.00675MaRDI QIDQ2411865

Tulasi Ram Reddy

Publication date: 25 October 2017

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.00675

zbMATH Keywords

zeroscritical pointsrandom polynomialsGauss-Lucas theoremrandom rational functions

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Convergence of probability measures (60B10)

Related Items (7)

Distances between zeroes and critical points for random polynomials with i.i.d. zeroes ⋮ Zeros of random polynomials and their higher derivatives ⋮ Free Convolution Powers Via Roots of Polynomials ⋮ Dynamics of Zeroes Under Repeated Differentiation ⋮ Almost sure behavior of the critical points of random polynomials ⋮ On the local pairing behavior of critical points and roots of random polynomials ⋮ Sums of random polynomials with independent roots

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