Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds: An addendum

Bernard Shiffman*, Steve Zelditch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We define a Gaussian measure on the space HJ0(M, LN) of almost holomorphic sections of powers of an ample line bundle L over a symplectic manifold (M, ω), and calculate the joint probability densities of sections taking prescribed values and covariant derivatives at a finite number of points. We prove that they have a universal scaling limit as N → ∞. This result will be used in another paper to extend our previous work on universality of scaling limits of correlations between zeros to the almost-holomorphic setting.

Original languageEnglish (US)
Pages (from-to)291-302
Number of pages12
JournalProceedings of the American Mathematical Society
Volume131
Issue number1
DOIs
StatePublished - Jan 2003

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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