Poincaré-Lelong approach to universality and scaling of correlations between zeros

Pavel Bleher*, Bernard Shiffman, Steve Zelditch

*Corresponding author for this work

Research output: Contribution to journalArticle

26 Scopus citations

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 LN 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 languageEnglish (US)
Pages (from-to)771-785
Number of pages15
JournalCommunications in Mathematical Physics
Volume208
Issue number3
DOIs
StatePublished - Jan 2000

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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