TY - JOUR

T1 - Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds

T2 - An addendum

AU - Shiffman, Bernard

AU - Zelditch, Steve

PY - 2003/1

Y1 - 2003/1

N2 - We define a Gaussian measure on the space HJ0(M, LN) 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.

AB - We define a Gaussian measure on the space HJ0(M, LN) 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.

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U2 - 10.1090/S0002-9939-02-06557-7

DO - 10.1090/S0002-9939-02-06557-7

M3 - Article

AN - SCOPUS:0037237323

SN - 0002-9939

VL - 131

SP - 291

EP - 302

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -