Connectivity in Sub-Poisson Networks

: We consider a class of point processes, which we call sub-Poisson; these are point processes that can be directionallyconvexly (dcx) dominated by some Poisson point process. The dcx order has already been shown in [4] useful in comparing various point process characteristics, including Ripley's and correlation functions as well as shot-noise fields generated by point processes, indicating in particular that smaller in the dcx order processes exhibit more regularity (less clustering, less voids) in the repartition of their points. Using these results, in this paper we study the impact of the dcx ordering of point processes on the properties of two continuum percolation models, which have been proposed in the literature to address macroscopic connectivity properties of large wireless networks. As the first main result of this paper, we extend the classical result on the existence of phase transition in the percolation of the Gilbert's graph (called also the Boolean model), ge...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Bartlomiej Blaszczyszyn, D. Yogeshwaran
• Keywords: CORR 2010, Education, Point Process, Point Processes, Poisson Point Process