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

Abstract

In this work, we introduce 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 process, while the vertices are the support of a Bernoulli 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. 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.