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

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, 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 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.