Universality and scaling of correlations between zeros on complex manifolds

Pavel Bleher*, Bernard Shiffman, Steve Zelditch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

97 Scopus citations

Abstract

We study the limit as N → ∞ of the correlations between simultaneous zeros of random sections of the powers LN of a positive holomorphic line bundle L over a compact complex manifold M, when distances are rescaled so that the average density of zeros is independent of N. We show that the limit correlation is independent of the line bundle and depends only on the dimension of M and the codimension of the zero sets. We also provide some explicit formulas for pair correlations. In particular, we prove that Hannay's limit pair correlation function for SU(2) polynomials holds for all compact Riemann surfaces.

Original languageEnglish (US)
Pages (from-to)351-395
Number of pages45
JournalInventiones Mathematicae
Volume142
Issue number2
DOIs
StatePublished - 2000

ASJC Scopus subject areas

  • Mathematics(all)

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