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Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds: An addendum
Author(s):
Bernard
Shiffman;
Steve
Zelditch
Journal:
Proc. Amer. Math. Soc.
131
(2003),
291-302.
MSC (2000):
Primary 53D50, 53D35, 60D05
Posted:
May 8, 2002
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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.
References:
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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:
10.1090/S0002-9939-02-06557-7
PII:
S 0002-9939(02)06557-7
Received by editor(s):
August 3, 2001
Posted:
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
Copyright of article:
Copyright
2002,
American Mathematical Society
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