Asymptotic Mass Distribution of Random Holomorphic Sections

2025/05/11 by Turgay Bayraktar, Bayraktar, Turgay, Afrim Bojnik +1
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Probability (math.PR)

paper · doi:10.48550/arxiv.2505.07120

openalex publication_date 2025/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove a central limit theorem for the mass distribution of random holomorphic sections associated with a sequence of positive line bundles endowed with \mathscrC³ Hermitian metrics over a compact Kähler manifold. In addition, we show that almost every sequence of such random holomorphic sections exhibits quantum ergodicity in the sense of Zelditch.

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