Variance Estimate of Systems of Random Holomorphic Sections in a Sequence of Line Bundles on Compact Kahler Manifolds

Abstract: This paper primarily concerns the variance estimate of zeros of systems of random holomorphic sections associated with a sequence of smooth Hermitian holomorphic line bundles on a compact Kahler manifold X. The probability measures taken into consideration in this paper satisfy a certain condition which makes it much more general(possibly the most general) than (all) the measures mostly studied in the literature. In particular we also give variance estimates for several known measures such as Gaussian and Fubini-Study measures.