inria-00372331, version 2
Percolation and Connectivity in AB Random Geometric Graphs
(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:
- Indian Institute of Science.
- 2:
- INRIA – Ecole normale supérieure de Paris - ENS Paris
- Domain : Mathematics/Probability
- Keywords : Random Geometric Graphs – Percolation – Connectivity.
- Comment : Submitted.
- Available versions : v1 (2009-04-01) v2 (2009-04-02) v3 (2010-01-23)
- inria-00372331, version 2
- http://hal.inria.fr/inria-00372331
- oai:hal.inria.fr:inria-00372331
- From:
- Submitted on: Thursday, 2 April 2009 18:42:00
- Updated on: Thursday, 2 April 2009 20:18:47
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