Asymptotic Mass Distribution of Random Holomorphic Sections

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

18 pages. v.2 Minor revisions. To appear in Anal. Math. Phys