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

2022/01/27 by Ozan Günyüz, Günyüz, Ozan
Mathematics · #Geometry and complex manifolds #Meromorphic and Entire Functions #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2201.11395

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.

Related

• Random Systems of Holomorphic Sections of a Sequence of Line bundles on Compact Kähler Manifolds
• Asymptotic expansion of the variance of random zeros on complex manifolds
• Equidistribution for Random Polynomials and Systems of Random Holomorphic Sections
• Number variance of random zeros
• Stochastic Kähler geometry: from random zeros to random metrics