Correlations and Pairing between Zeros and Critical Points of Gaussian Random Polynomials

DOI10.1093/imrn/rnt192zbMath1341.60019arXiv1207.4734OpenAlexW3099070706MaRDI QIDQ5174211

Boris Hanin

Publication date: 17 February 2015

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4734

zbMATH Keywords

zeroscritical pointsGaussian random polynomials

Mathematics Subject Classification ID

Gaussian processes (60G15) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Limit theorems in probability theory (60F99)

Related Items (12)

Variance of the number of zeroes of shift-invariant Gaussian analytic functions ⋮ Distances between zeroes and critical points for random polynomials with i.i.d. zeroes ⋮ On the geometry of random lemniscates ⋮ Unnamed Item ⋮ Zeros of random polynomials and their higher derivatives ⋮ Dynamics of Zeroes Under Repeated Differentiation ⋮ On the local pairing behavior of critical points and roots of random polynomials ⋮ Correlations between zeros and critical points of random analytic functions ⋮ Pairing between zeros and critical points of random polynomials with independent roots ⋮ Critical points of holomorphic sections of line bundles and a spherical Gauss-Lucas theorem ⋮ The lemniscate tree of a random polynomial ⋮ Asymptotic expansion of the off-diagonal Bergman kernel on compact Kähler manifolds

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