Iyer, Srikanth K and Yogeshwaran, D (2012) Percolation and connectivity in AB random geometric graphs. In: ADVANCES IN APPLIED PROBABILITY, 44 (1). pp. 2141.

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Abstract
Given two independent Poisson point processes Phi((1)), Phi((2)) in Rd, the AB Poisson Boolean model is the graph with the points of Phi((1)) as vertices and with edges between any pair of points for which the intersection of balls of radius 2r centered at these points contains at least one point of Phi((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 fora 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 tau n in the unit cube. The AB random geometric graph is defined as above but with balls of radius r. We derive a weak law result for the largest nearestneighbor distance and almostsure asymptotic bounds for the connectivity threshold.
Item Type:  Journal Article 

Publication:  ADVANCES IN APPLIED PROBABILITY 
Publisher:  APPLIED PROBABILITY TRUST, THE UNIVERSITY, SCHOOL MATHEMATICS STATISTICS, SHEFFIELD S3 7RH, ENGLAND 
Department/Centre:  Division of Physical & Mathematical Sciences > Mathematics 
Date Deposited:  30 Jul 2012 12:18 
Last Modified:  30 Jul 2012 12:18 
URI:  http://eprints.iisc.ac.in/id/eprint/44527 
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