Bernoulli

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

Macroscopic analysis of determinantal random balls

Jean-Christophe Breton, Adrien Clarenne, and Renan Gobard

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

Permanent link to this document
https://projecteuclid.org/euclid.bj/1551862860

Digital Object Identifier
doi:10.3150/18-BEJ1030

Mathematical Reviews number (MathSciNet)
MR3920382

Zentralblatt MATH identifier
07049416

Keywords
determinantal point processes generalized random fields limit theorem point processes stable fields

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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