Weihong Yao, Distribution
of Normalized Zero-Sets of Random Entire Functions Abstract This paper is concerned with the distribution of
normalized zero-sets of random entire functions. The normalization of the
zero-set is performed in the same way as that of the counting function for an
entire function in Nevanlinna theory. The results
generalize the Shiffman and Zelditch
theory on the distribution of the zeroes of random holomorphic
sections of powers for positive Hermitian holomorphic line bundles from polynomial functions to
entire functions. Our results can also be viewed as the generalization of Nevanlinna's First Main Theorem in the theory of the
distribution of zero-sets of random entire functions. |