Precise Deviations for Disk Counting Statistics of Invariant Determinantal Processes

Abstract We consider 2-dimensional determinantal processes that are rotationinvariant and study the fluctuations of number points in disks. Based on theory mod-phi convergence, we obtain Berry–Esseen as well precise moderate to large deviation estimates for these statistics. These results consistent with Coulomb gas heuristic from physics literature. also functional limit theorems stochastic process $(\# D_r)_{r>0}$ when radius $r$ disk $D_r$ is growing different regimes. present several applications invariant processes, including polyanalytic Ginibre ensembles, zeros hyperbolic Gaussian analytic function, other models. As a corollary, compute asymptotics entanglement entropy (integer) Laughlin states all Landau levels.