Volume fluctuations of random analytic varieties in the unit ball Xavier MassanedaBharti Pridhnani 32A1060G99Hyperbolic Gaussian analytic functions Given a Gaussian analytic function $f_L$ of intesity $L$ in the unit ball of $\mathbb{C}^n$, $n\geq2$, consider its (random) zero variety $Z(f_L)$. We reduce the variance of the $(n-1)$-dimensional volume of $Z(f_L)$ 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 $r\to1^{-}$ and as $L\to\infty$. Both the results and the proofs generalise to the ball those given by Jeremiah Buckley for the unit disk. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5693 10.1512/iumj.2015.64.5693 en Indiana Univ. Math. J. 64 (2015) 1667 - 1695 state-of-the-art mathematics http://iumj.org/access/