On the zeros of random harmonic polynomials: the truncated model

DOI10.1016/j.jmaa.2016.02.039zbMath1334.31001arXiv1507.01041OpenAlexW2281581131MaRDI QIDQ252934

Erik Lundberg, Antonio Lerario

Publication date: 4 March 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.01041

zbMATH Keywords

harmonic polynomialsKac-Rice formularandom polynomialsWilmshurst's conjecture

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) 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 (10)

About the cover: visualization of harmonic functions ⋮ The valence of harmonic polynomials viewed through the probabilistic lens ⋮ On the geometry of random lemniscates ⋮ On the zeros of random harmonic polynomials: the Weyl model ⋮ Inradius of random lemniscates ⋮ On the numbers of images of two stochastic gravitational lensing models ⋮ A Survey on the Maximal Number of Solutions of Equations Related to Gravitational Lensing ⋮ Zeros of harmonic polynomials, critical lemniscates, and caustics ⋮ Asymptotic variance of the number of real roots of random polynomial systems ⋮ Location of the zeros of harmonic trinomials

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