Massaneda Clares, Francesc XavierPridhnani, Bharti2023-01-242023-01-242015-11-230022-2518https://hdl.handle.net/2445/192549Given a Gaussian analytic function $f_L$ of intesity $L$ in the unit ball of $\mathbb{C}^n, n \geq 2$, consider its (random) zero variety $Z\left(f_L\right)$. We reduce the variance of the $(n-1)$-dimensional volume of $Z\left(f_L\right)$ inside a pseudo-hyperbolic ball of radius $r$ to an integral of a positive function in the unit disk. We illustrate the usefulness of this expression by describing the asymptotic behaviour of the variance as $r \rightarrow 1^{-}$and as $L \rightarrow \infty$. Both the results and the proofs generalise to the ball those given by Jeremiah Buckley for the unit disk.29 p.application/pdfeng(c) Indiana University Mathematics Journal, 2015Espais analíticsProcessos gaussiansAnalytic spacesGaussian processesinfo:eu-repo/semantics/article6444262023-01-24info:eu-repo/semantics/openAccess