A survey on asymptotic equilibrium distribution of zeros of random holomorphic sections

Duc-Viet Vu; George Marinescu

A survey on asymptotic equilibrium distribution of zeros of random holomorphic sections

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arxiv 2504.15083 v1 pith:PZL4WKQ5 submitted 2025-04-21 math.CV math.PR

George Marinescu , Duc-Viet Vu This is my paper · ORCID

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keywords holomorphicasymptoticdistributionequilibriumrandomsectionssurveyzeros

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This is a survey of results concerning the asymptotic equilibrium distribution of zeros of random holomorphic polynomials and holomorphic sections of high powers of a positive line bundle, as related to the authors' recent work. Our primary focus is on the role of pluripotential theory in this research area.

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Bernstein-Markov measures and Toeplitz theory
math.CV 2025-06 conditional novelty 7.0 of 10

For Bernstein-Markov measures on big line bundles, Bergman measures concentrate on the diagonal and Toeplitz operators close under composition, with spectra governed by the equilibrium measure.

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