Macroscopic analysis of determinantal random balls

TL;DR

This paper analyzes a model of Euclidean random balls generated by a determinantal point process, revealing that at a macroscopic level, the interactions are lost and the behavior resembles classical regimes like Gaussian, Poissonian, and stable.

Contribution

It demonstrates that the macroscopic limit of determinantal random balls converges to classical regimes, showing interaction effects vanish at large scales.

Findings

Macroscopic regimes include Gaussian, Poissonian, and stable.

Interactions induced by the determinantal process are erased at large scales.

The model generalizes the Poissonian case to include interactions.

Abstract

We consider a collection of Euclidean random balls in ${\Bbb R}^d$ generated by a determinantal point process inducing interaction into the balls. We study this model at a macros\-copic 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.