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inria-00372331, version 2

## Percolation and Connectivity in AB Random Geometric Graphs

Srikanth K. Iyer () 1, D. Yogeshwaran () 2

(2009)

Abstract: We study a generalization to the continuum of the $AB$ percolation model on discrete lattices. Let $\Pl,\Pm$ be independent Poisson point processes in $\mR^d$, $d \geq 2,$ of intensities $\lambda, \mu$ respectively. The $AB$ random geometric graph $G(\lam, \mu, r)$ is a graph whose vertex set is $\Pl$ with edges between any two points $X_i, X_j \in \Pl$ provided there exists a $Y \in \Pm$ such that $|X_k - Y| \leq r$, $k=i, j$. We investigate percolation and connectivity in $AB$ random geometric graphs.

• 1:  Departement of Mathematics (IISc)
• Indian Institute of Science.
• 2:  TREC (INRIA Rocquencourt)
• INRIA – Ecole normale supérieure de Paris - ENS Paris

• inria-00372331, version 2
• oai:hal.inria.fr:inria-00372331
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• Submitted on: Thursday, 2 April 2009 18:42:00
• Updated on: Thursday, 2 April 2009 20:18:47