Asymptotic Mass Distribution of Random Holomorphic Sections
Complex Variables
2025-12-24 v2 Differential Geometry
Probability
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 Hermitian metrics over a compact K\"{a}hler manifold. In addition, we show that almost every sequence of such random holomorphic sections exhibits quantum ergodicity in the sense of Zelditch.
Cite
@article{arxiv.2505.07120,
title = {Asymptotic Mass Distribution of Random Holomorphic Sections},
author = {Turgay Bayraktar and Afrim Bojnik},
journal= {arXiv preprint arXiv:2505.07120},
year = {2025}
}
Comments
18 pages. v.2 Minor revisions. To appear in Anal. Math. Phys