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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
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.
References:
-
- [Arc]
- Archimedes, On the Sphere and Cylinder (Greek), Syracuse, ca. 257BC.
- [Aur]
- Denis Auroux, Estimated transversality in symplectic geometry and projective maps, to appear in Proc. International KIAS Conference (Seoul, 2000), http://xxx.lanl.gov/abs/math.SG/0010052.
- [BSZ1]
- P. Bleher, B. Shiffman and S. Zelditch, Universality and scaling of correlations between zeros on complex manifolds, Invent. Math. 142 (2000), 351-395.
- [BSZ2]
- P. Bleher, B. Shiffman and S. Zelditch, Universality and scaling of zeros on symplectic manifolds, in Random Matrix Models and Their Applications, P. Bleher and A. Its (Eds.), MSRI Publications 40, Cambridge Univ. Press, 2001, pp. 31-69.
- [BSZ3]
- P. Bleher, B. Shiffman and S. Zelditch, Correlations between zeros and supersymmetry, Commun. Math. Phys. 224 (2001), 255-269.
- [BoGu]
- L. Boutet de Monvel and V. Guillemin, The Spectral Theory of Toeplitz Operators, Ann. Math. Studies 99, Princeton Univ. Press, Princeton, 1981. MR 85j:58141
- [BoSj]
- L. Boutet de Monvel and J. Sjöstrand, Sur la singularité des noyaux de Bergman et de Szegö, Asterisque 34-35 (1976), 123-164. MR 58:28684
- [Don]
- S. K. Donaldson, Symplectic submanifolds and almost complex geometry, J. Diff. Geom. 44 (1996), 666-705. MR 98h:53045
- [ShZe1]
- B. Shiffman and S. Zelditch, Random almost holomorphic sections of ample line bundles on symplectic manifolds, (preprint 2000), http://xxx.lanl.gov/abs/math.SG/0001102.
- [ShZe2]
- B. Shiffman and S. Zelditch, Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds, J. Reine Angew. Math. 544 (2002), 181-222.
- [ShZe3]
- B. Shiffman and S. Zelditch, Random polynomials and Levy concentration of measure, (in preparation).
- [Woo]
- N. M. J. Woodhouse, Geometric Quantization, Clarendon Press, Oxford, 1992. MR 94a:58082
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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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