Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds: An addendum
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- by Bernard Shiffman and Steve Zelditch PDF
- Proc. Amer. Math. Soc. 131 (2003), 291-302 Request permission
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.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
- MR Author ID: 186875
- Email: zelditch@math.jhu.edu
- 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
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1929049