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<p>We present an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Riemann surface. We prove several results for the zeros of Gaussian holomorphic sections in the semi-classical limit, including the equidistribution, large deviation estimates, central limit theorem, and number variances.</p>

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Semipositive line bundles on punctured Riemann surfaces: Bergman kernels and random zeros

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月25日

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  • Bingxiao Liu,
  • Dominik Zielinski

摘要

We present an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Riemann surface. We prove several results for the zeros of Gaussian holomorphic sections in the semi-classical limit, including the equidistribution, large deviation estimates, central limit theorem, and number variances.