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

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dc.creatorShiffman, B.
dc.creatorZelditch, S.
dc.date2002-12-12
dc.date.accessioned2026-07-07T04:53:45Z
dc.date.available2026-07-07T04:53:45Z
dc.descriptionWe 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 $(M, ω)$, 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 completes our proof (with P. Bleher) that correlations between zeros of sections in the almost-holomorphic setting have the same universal scaling limit as in the complex case (see Universality and scaling of zeros on symplectic manifolds, Random matrix models and their applications, 31--69, Math. Sci. Res. Inst. Publ., 40)
dc.descriptionAddendum to math.SG/0212180. Supplements and completes results of math-ph/0002039
dc.identifierhttps://arxiv.org/abs/math/0212181
dc.identifierhttp://arxiv.org/abs/math/0212181
dc.identifierProc. Amer. Math. Soc. 131 (2003), no. 1, 291--302
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65978
dc.subjectSymplectic Geometry
dc.subjectProbability
dc.subject53C15
dc.titleAsymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds: an addendum
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