The Distribution of Zeros of the Derivative of a Random Polynomial

DOI10.1007/978-3-642-30979-3_14zbMath1272.30004arXiv1109.5975OpenAlexW1890931827MaRDI QIDQ2846965

Igor Rivin, Robin Pemantle

Publication date: 4 September 2013

Published in: Advances in Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.5975

zbMATH Keywords

critical pointsrandom polynomialsGauss-Lucas theoremGaussian series

Mathematics Subject Classification ID

Polynomials and rational functions of one complex variable (30C10) Random power series in one complex variable (30B20)

Related Items (17)

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 ⋮ 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 ⋮ Pairing between zeros and critical points of random polynomials with independent roots ⋮ Sums of random polynomials with independent roots ⋮ Zeros of derivatives of Gaussian random polynomials on plane domains ⋮ Some recent results on the geometry of complex polynomials: the Gauss-Lucas theorem, polynomial lemniscates, shape analysis, and conformal equivalence ⋮ Leaky roots and stable Gauss-Lucas theorems ⋮ A nonlocal transport equation describing roots of polynomials under differentiation ⋮ Critical points of random polynomials with independent identically distributed roots ⋮ Higher-order, polar and Sz.-Nagy's generalized derivatives of random polynomials with independent and identically distributed zeros on the unit circle ⋮ A nonlocal transport equation modeling complex roots of polynomials under differentiation

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