Asymptotic Mass Distribution of Random Holomorphic Sections

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 ${\mathcal{C}}^3$ 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.