Rescaled weighted determinantal random balls

TL;DR

This paper studies a model of weighted random balls in Euclidean space with repulsive point process distribution, analyzing the effects of scaling on the spatial structure and revealing regimes similar to Poisson models.

Contribution

It introduces a rescaling analysis of determinantal random balls, showing how repulsion diminishes under zoom-out, aligning with Poissonian behavior in the limit.

Findings

Repulsion between balls diminishes under zoom-out.

Three regimes of behavior are identified, matching Poissonian case.

The model bridges determinantal and Poisson point processes.

Abstract

We consider a collection of weighted Euclidian random balls in R^d distributed according a determinantal point process. We perform a zoom-out procedure by shrinking the radii while increasing the number of balls. We observe that the repulsion between the balls is erased and three different regimes are obtained, the same as in the weighted Poissonian case.