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

2002/12/12 by B. Shiffman, S. Zelditch · 2 citations
Mathematics · #math.SG #math.PR #msc:53C15

paper · pdf

published as Proc. Amer. Math. Soc. 131 (2003), no. 1, 291--302 · Addendum to math.SG/0212180. Supplements and completes results of math-ph/0002039

arxiv created 2002/12/12 · arxiv updated 2009/11/30

Abstract

We define a Gaussian measure on the space H⁰_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 → ∞. 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)

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