Continuum Line-of-Sight Percolation on Poisson-Voronoi Tessellations

Quentin Le Gall 1 Bartłomiej Błaszczyszyn 2 Elie Cali 1 Taoufik En-Najjary 3
2 DYOGENE - Dynamics of Geometric Networks
Inria de Paris, CNRS - Centre National de la Recherche Scientifique : UMR 8548, DI-ENS - Département d'informatique de l'École normale supérieure
Abstract : In this work, we study a new model for continuum line-of-sight percolation in a random environment given by a Poisson-Voronoi tessellation. The edges of this tessellation are the support of a Cox point process, while the vertices are the support of a Bernoulli point process. Taking the superposition $Z$ of these two processes, two points of $Z$ are linked by an edge if and only if they are sufficiently close and located on the same edge of the supporting tessellation. We study the percolation of the random graph arising from this construction and prove that a subcritical phase as well as a supercritical phase exist under general assumptions. Our proofs are based on a renormalization argument with some notion of stabilization and asymptotic essential connectedness to investigate continuum percolation for Cox point processes. We also give numerical estimates of the critical parameters of the model. Our model can be seen as a good candidate for modelling telecommunications networks in a random environment with obstructive conditions for signal propagation.
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https://hal.inria.fr/hal-02192469
Contributor : Bartlomiej Blaszczyszyn <>
Submitted on : Tuesday, July 23, 2019 - 6:18:58 PM
Last modification on : Friday, October 18, 2019 - 2:38:03 PM

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  • HAL Id : hal-02192469, version 1
  • ARXIV : 1904.10875

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Quentin Le Gall, Bartłomiej Błaszczyszyn, Elie Cali, Taoufik En-Najjary. Continuum Line-of-Sight Percolation on Poisson-Voronoi Tessellations. 2019. ⟨hal-02192469⟩

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