### 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 language | English (US) |
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Pages (from-to) | 3765-3791 |

Number of pages | 27 |

Journal | Transactions of the American Mathematical Society |

Volume | 373 |

Issue number | 6 |

DOIs | |

State | Published - 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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## Cite this

Bayraktar, T., Coman, D., & Marinescu, G. (2020). Universality results for zeros of random holomorphic sections.

*Transactions of the American Mathematical Society*,*373*(6), 3765-3791. https://doi.org/10.1090/tran/7807