Gaussian Analytic functions in the unit ball

Abstract

We study some properties of hyperbolic Gaussian analytic functions of intensity $L$ in the unit ball of ${\mathbb{C}}^n$. First we deal with the asymptotics of fluctuations of linear statistics as $L\to \infty$. Then we estimate the probability of large deviations (with respect to the expected value) of such linear statistics and use this estimate to prove a hole theorem.

25 pages

References in corpus (1)

• Fluctuations in the zero set of the hyperbolic Gaussian analytic function