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 result generalizes 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 result can also be viewed as the analogy of Nevanlinna's First Main Theorem in the theory of the distribution of zero-sets of random entire functions.