Universality results for zeros of random holomorphic sections

Turgay Bayraktar, Dan Coman, George Marinescu

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

In this work we prove a universality result regarding the equidistribution of zeros of random holomorphic sections associated to a sequence of singular Hermitian holomorphic line bundles on a compact Kähler complex space X. Namely, under mild moment assumptions, we show that the asymptotic distribution of zeros of random holomorphic sections is independent of the choice of the probability measure on the space of holomorphic sections. In the case when X is a compact Kähler manifold, we also prove an off-diagonal exponential decay estimate for the Bergman kernels of a sequence of positive line bundles on X.

Original languageEnglish (US)
Pages (from-to)3765-3791
Number of pages27
JournalTransactions of the American Mathematical Society
Volume373
Issue number6
DOIs
StatePublished - Jun 2020

Keywords

  • Bergman kernel
  • Compact normal Kähler complex space
  • Fubini-Study current
  • Singular Hermitian metric
  • Zeros of random holomorphic sections

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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