Pairing between zeros and critical points of random polynomials with independent roots

DOI10.1090/tran/7496zbMath1426.30006arXiv1610.06248OpenAlexW2962850448MaRDI QIDQ4645087

Noah Williams, Sean O'Rourke

Publication date: 10 January 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.06248

zbMATH Keywords

critical pointsempirical distributionrandom polynomialszeros of the derivativeoutlier critical points

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) Random measures (60G57) Convergence of probability measures (60B10)

Related Items (13)

Distances between zeroes and critical points for random polynomials with i.i.d. zeroes ⋮ The flow of polynomial roots under differentiation ⋮ Unnamed Item ⋮ 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 ⋮ A STABILITY VERSION OF THE GAUSS–LUCAS THEOREM AND APPLICATIONS ⋮ Sums of random polynomials with independent roots ⋮ The lemniscate tree of a random polynomial ⋮ A nonlocal transport equation describing roots of polynomials under differentiation ⋮ A nonlocal transport equation modeling complex roots of polynomials under differentiation

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