Pairing of zeros and critical points for random polynomials

DOI10.1214/16-AIHP767zbMath1373.30006arXiv1601.06417OpenAlexW2963049380MaRDI QIDQ2403227

Boris Hanin

Publication date: 15 September 2017

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.06417

zbMATH Keywords

zeroscritical pointsrandom polynomialsGauss-Lucas

Mathematics Subject Classification ID

Random fields (60G60) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Polynomials and rational functions of one complex variable (30C10)

Related Items (14)

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 ⋮ On the local pairing behavior of critical points and roots of random polynomials ⋮ A STABILITY VERSION OF THE GAUSS–LUCAS THEOREM AND APPLICATIONS ⋮ Correlations between zeros and critical points of random analytic functions ⋮ Pairing between zeros and critical points of random polynomials with independent roots ⋮ 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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