Determinantal random balls model
Résumé
In this work, we propose a random balls model on $\mathbb{C}$ generated by a determinantal point process. We use a Ginibre point process to generate the centers of the balls and thus we introduce repulsion phenomena between the balls. Studying the model at a macroscopic level allows us to extend the results obtained for random balls models generated by a Poisson point process. Indeed, we obtain three different limit fields : the first one is a Gaussian integral, the second one is a stable integral and the last one is a Poissonian integral that bridges between the two previous ones.