Fluctuations of the process of moduli for the Ginibre and hyperbolic ensembles

In this talk, we investigate the point process of moduli of the Ginibre and hyperbolic ensembles. We show that far from the origin and at an appropriate scale, these processes exhibit Gaussian and Poisson fluctuations. Among the possible Gaussian fluctuations, we can find white noise but also fluctuations with non-trivial covariance at a particular scale. This talk is based on a joint work with Prof. Alexander I. Bufetov and Prof. David García-Zelada.