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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathscr {C}^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="script">C</mi> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> 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.</p>

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Asymptotic mass distribution of random holomorphic sections

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月20日

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  • Turgay Bayraktar,
  • Afrim Bojnik

摘要

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 \(\mathscr {C}^{3}\) 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.