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May 2019 Macroscopic analysis of determinantal random balls
Jean-Christophe Breton, Adrien Clarenne, Renan Gobard
Bernoulli 25(2): 1568-1601 (May 2019). DOI: 10.3150/18-BEJ1030

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.

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Jean-Christophe Breton. Adrien Clarenne. Renan Gobard. "Macroscopic analysis of determinantal random balls." Bernoulli 25 (2) 1568 - 1601, May 2019. https://doi.org/10.3150/18-BEJ1030

Information

Received: 1 June 2017; Revised: 1 October 2017; Published: May 2019
First available in Project Euclid: 6 March 2019

zbMATH: 07049416
MathSciNet: MR3920382
Digital Object Identifier: 10.3150/18-BEJ1030

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 2 • May 2019
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