### Abstract

This note is concerned with the scaling limit as N → ∞ of n-point correlations between zeros of random holomorphic polynomials of degree N in m variables. More generally we study correlations between zeros of holomorphic sections of powers L^{N} of any positive holomorphic line bundle L over a compact Kähler manifold. Distances are rescaled so that the average density of zeros is independent of N. Our main result is that the scaling limits of the correlation functions and, more generally, of the "correlation forms" are universal, i.e. independent of the bundle L, manifold M or point on M.

Original language | English (US) |
---|---|

Pages (from-to) | 771-785 |

Number of pages | 15 |

Journal | Communications in Mathematical Physics |

Volume | 208 |

Issue number | 3 |

DOIs | |

State | Published - Jan 2000 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

## Fingerprint Dive into the research topics of 'Poincaré-Lelong approach to universality and scaling of correlations between zeros'. Together they form a unique fingerprint.

## Cite this

Bleher, P., Shiffman, B., & Zelditch, S. (2000). Poincaré-Lelong approach to universality and scaling of correlations between zeros.

*Communications in Mathematical Physics*,*208*(3), 771-785. https://doi.org/10.1007/s002200050010