Zeros of conditional Gaussian analytic functions, random sub-unitary matrices and q-series

Yan V. Fyodorov, Boris A. Khoruzhenko, Thomas Prellberg

We investigate radial statistics of zeros of hyperbolic Gaussian Analytic Functions (GAF) of the form $\ddot{I}†(z)={\sum }_{k\ge 0}{c}_k{z}^k$ given that $|\ddot{I}†(0){|}^2=t$ and assuming coeffici…