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

DOI:
https://doi.org/10.1090/S0002-9939-02-06557-7

Published electronically:
May 8, 2002

MathSciNet review:
1929049

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Abstract: We define a Gaussian measure on the space of almost holomorphic sections of powers of an ample line bundle over a symplectic manifold , 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 . 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:
https://doi.org/10.1090/S0002-9939-02-06557-7

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