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Inventiones mathematicae

, Volume 142, Issue 2, pp 351–395 | Cite as

Universality and scaling of correlations between zeros on complex manifolds

  • Pavel Bleher
  • Bernard Shiffman
  • Steve Zelditch

Abstract.

We study the limit as N→∞ of the correlations between simultaneous zeros of random sections of the powers L N 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.

Keywords

Manifold Correlation Function Riemann Surface Line Bundle Explicit Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Pavel Bleher
    • 1
  • Bernard Shiffman
    • 2
  • Steve Zelditch
    • 2
  1. 1.Department of Mathematical Sciences, IUPUI, Indianapolis, IN 46202, USA¶(e-mail: bleher@math.iupui.edu)US
  2. 2.Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA¶(e-mail: shiffman@math.jhu.edu, zel@math.jhu.edu)US

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