Gaussian Analytic functions in the unit ball
  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. 
Jeremiah Buckley, Xavier Massaneda, Bharti Pridhnani
math.CV