Abstract
Continuum percolation models in which each point of a two-dimensional Poisson point process is the centre of a disc of given (or random) radius
We look at the percolation properties of this generalized model, showing that an unbounded connected component of discs does not exist, almost surely, for small values of the density
We show how a simple scaling operation can change the percolation properties of the model, leading to the almost sure existence of an unbounded connected component for large values of
Finally, we show that a large class of covering algorithms, which arise in many practical applications, can get arbitrarily close to achieving a minimal density of covering discs. We also construct an algorithm that achieves this minimal density.
Citation
Lorna Booth. Jehoshua Bruck. Massimo Franceschetti. Ronald Meester. "Covering algorithms, continuum percolation and the geometry of wireless networks." Ann. Appl. Probab. 13 (2) 722 - 741, May 2003. https://doi.org/10.1214/aoap/1050689601
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