Percolation and Connectivity in AB Random Geometric Graphs

Iyer, Srikanth K and Yogeshwaran, D (2010) Percolation and Connectivity in AB Random Geometric Graphs. TR-PME-2010-17.

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Abstract

Given two independent Poisson point processes ©(1);©(2) in Rd, the AB Poisson Boolean model is the graph with points of ©(1) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centred at these points contains at least one point of ©(2). This is a generalization of the AB percolation model on discrete lattices. We show the existence of percolation for all d ¸ 2 and derive bounds for a critical intensity. We also provide a characterization for this critical intensity when d = 2. To study the connectivity problem, we consider independent Poisson point processes of intensities n and cn in the unit cube. The AB random geometric graph is de¯ned as above but with balls of radius r. We derive a weak law result for the largest nearest neighbour distance and almost sure asymptotic bounds for the connectivity threshold.

Item Type:	Departmental Technical Report
Keywords:	Random geometric graph;percolation;connectivity;wireless networks;secure commu-nication.
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering > Electrical Communication Engineering - Technical Reports
Date Deposited:	08 Sep 2011 11:46
Last Modified:	08 Sep 2011 11:46
URI:	http://eprints.iisc.ac.in/id/eprint/40378

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