Macroscopic analysis of determinantal random balls

Abstract

We consider a collection of Euclidean random balls in $\mathbb{R}^{d}$ generated by a determinantal point process inducing inhibitory interaction into the balls. We study this model at a macroscopic level obtained by a zooming-out and three different regimes – Gaussian, Poissonian and stable – are exhibited as in the Poissonian model without interaction. This shows that the macroscopic behaviour erases the interactions induced by the determinantal point process.