This note demonstrates the asymptotic mass distribution in random holomorphic sections, suggesting a link to quantum ergodicity.
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 C³ 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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Bayraktar et al. (2026) studied this question.
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