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 -