Buckley, JeremiahMassaneda Clares, Francesc XavierPridhnani, Bharti2023-01-242023-01-242015-11-030021-2172https://hdl.handle.net/2445/192551We 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 $L \rightarrow \infty$. 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.27 p.application/pdfeng(c) Springer Verlag, 2015Funcions holomorfesFuncions de variables complexesRepresentacions integralsTeoremes de límit (Teoria de probabilitats)Processos gaussiansHolomorphic functionsFunctions of complex variablesIntegral representationsLimit theorems (Probability theory)Gaussian processesinfo:eu-repo/semantics/article6444272023-01-24info:eu-repo/semantics/openAccess