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

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

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


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.

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