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

Shiffman, Bernard; Zelditch, Steve

doi:10.1090/S0002-9939-02-06557-7

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

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