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Asymptotic Mass Distribution of Random Holomorphic Sections
Turgay Bayraktar, Afrim Bojnik · 2025-05-12 · via math.PR updates on arXiv.org

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 $\mathscr{C}^3$ 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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