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March 2012 Percolation and connectivity in AB random geometric graphs
Srikanth K. Iyer, D. Yogeshwaran
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Adv. in Appl. Probab. 44(1): 21-41 (March 2012). DOI: 10.1239/aap/1331216643

Abstract

Given two independent Poisson point processes Φ(1), Φ(2) in Rd, the AB Poisson Boolean model is the graph with the points of Φ(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 Φ(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 τn 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 nearest-neighbor distance and almost-sure asymptotic bounds for the connectivity threshold.

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Srikanth K. Iyer. D. Yogeshwaran. "Percolation and connectivity in AB random geometric graphs." Adv. in Appl. Probab. 44 (1) 21 - 41, March 2012. https://doi.org/10.1239/aap/1331216643

Information

Published: March 2012
First available in Project Euclid: 8 March 2012

zbMATH: 1248.60016
MathSciNet: MR2951545
Digital Object Identifier: 10.1239/aap/1331216643

Subjects:
Primary: 05C80, 60D05
Secondary: 05C40, 82B43

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 1 • March 2012
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