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May 2020 The maximal degree in a Poisson–Delaunay graph
Gilles Bonnet, Nicolas Chenavier
Bernoulli 26(2): 948-979 (May 2020). DOI: 10.3150/19-BEJ1123

Abstract

We investigate the maximal degree in a Poisson–Delaunay graph in $\mathbf{R}^{d}$, $d\geq 2$, over all nodes in the window $\mathbf{W}_{\rho }:=\rho^{1/d}[0,1]^{d}$ as $\rho $ goes to infinity. The exact order of this maximum is provided in any dimension. In the particular setting $d=2$, we show that this quantity is concentrated on two consecutive integers with high probability. A weaker version of this result is discussed when $d\geq 3$.

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Gilles Bonnet. Nicolas Chenavier. "The maximal degree in a Poisson–Delaunay graph." Bernoulli 26 (2) 948 - 979, May 2020. https://doi.org/10.3150/19-BEJ1123

Information

Received: 1 June 2018; Revised: 1 March 2019; Published: May 2020
First available in Project Euclid: 31 January 2020

zbMATH: 07166553
MathSciNet: MR4058357
Digital Object Identifier: 10.3150/19-BEJ1123

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 2 • May 2020
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