Open Access
November 2016 Quantifying repulsiveness of determinantal point processes
Christophe Ange Napoléon Biscio, Frédéric Lavancier
Bernoulli 22(4): 2001-2028 (November 2016). DOI: 10.3150/15-BEJ718


Determinantal point processes (DPPs) have recently proved to be a useful class of models in several areas of statistics, including spatial statistics, statistical learning and telecommunications networks. They are models for repulsive (or regular, or inhibitive) point processes, in the sense that nearby points of the process tend to repel each other. We consider two ways to quantify the repulsiveness of a point process, both based on its second-order properties, and we address the question of how repulsive a stationary DPP can be. We determine the most repulsive stationary DPP, when the intensity is fixed, and for a given $R>0$ we investigate repulsiveness in the subclass of $R$-dependent stationary DPPs, that is, stationary DPPs with $R$-compactly supported kernels. Finally, in both the general case and the $R$-dependent case, we present some new parametric families of stationary DPPs that can cover a large range of DPPs, from the stationary Poisson process (the case of no interaction) to the most repulsive DPP.


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Christophe Ange Napoléon Biscio. Frédéric Lavancier. "Quantifying repulsiveness of determinantal point processes." Bernoulli 22 (4) 2001 - 2028, November 2016.


Received: 1 July 2014; Revised: 1 February 2015; Published: November 2016
First available in Project Euclid: 3 May 2016

zbMATH: 1343.60058
MathSciNet: MR3498021
Digital Object Identifier: 10.3150/15-BEJ718

Keywords: $R$-dependent point process , compactly supported covariance function , covariance function , pair correlation function

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 4 • November 2016
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