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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Bernard Shiffman and Steve Zelditch
Journal: Proc. Amer. Math. Soc. 131 (2003), 291-302
MSC (2000): Primary 53D50, 53D35, 60D05
Published electronically: May 8, 2002
MathSciNet review: 1929049
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Abstract | References | Similar Articles | Additional Information

Abstract: We define a Gaussian measure on the space $H^0_J(M, L^N)$ of almost holomorphic sections of powers of an ample line bundle $L$ over a symplectic manifold $(M, \omega)$, 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 $N \to \infty$. 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.


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Additional Information

Bernard Shiffman
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
Email: shiffman@math.jhu.edu

Steve Zelditch
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
Email: zelditch@math.jhu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06557-7
PII: S 0002-9939(02)06557-7
Received by editor(s): August 3, 2001
Published electronically: May 8, 2002
Additional Notes: Research partially supported by NSF grants #DMS-9800479, #DMS-0100474 (first author) and #DMS-0071358 (second author).
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2002 American Mathematical Society