## Bernoulli

• Bernoulli
• Volume 25, Number 2 (2019), 1568-1601.

### 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.

#### Article information

Source
Bernoulli, Volume 25, Number 2 (2019), 1568-1601.

Dates
Revised: October 2017
First available in Project Euclid: 6 March 2019

https://projecteuclid.org/euclid.bj/1551862860

Digital Object Identifier
doi:10.3150/18-BEJ1030

Mathematical Reviews number (MathSciNet)
MR3920382

Zentralblatt MATH identifier
07049416

#### Citation

Breton, Jean-Christophe; Clarenne, Adrien; Gobard, Renan. Macroscopic analysis of determinantal random balls. Bernoulli 25 (2019), no. 2, 1568--1601. doi:10.3150/18-BEJ1030. https://projecteuclid.org/euclid.bj/1551862860

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