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Stochastic geometric networks : connectivity and comparison.

D. Yogeshwaran 1
1 TREC - Theory of networks and communications
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt
Abstract : The thesis comprises of two themes : 1)Percolation and connectivity of AB Random geometric graphs. Directionally convex ordering of point processes and its impact on percolation and connectivity. Under the first topic, we define a spatial bipartite graph called the AB Random geometric graph on two independent Poisson point processes. This is an extension of the discrete AB percolation model. We show the existence of percolation in all dimensions as well as obtain the bounds for the critical intensity. Further, in two dimensions, we characterise the critical intensity. For the problem of connectivity, we study the graph on two independent Poisson point processes on the unit cube with intensities n and cn for a constant c > 0. We give almost sure asymptotic bounds for the connectivity distance. The second subject aims to expound on the relate the afore-mentioned order on point processes to their clustering properties and its applications to performance characteristics of wireless networks. Firstly, the impact of the order on shot-noise fields are studied and using this, we give comparison results for critical radii for percolation of directionally convex ordered point processes. We conclude by showing that the processes which are lesser in directionally convex order than Poisson point process exhibit a non-trivial phase transition in many percolation models.
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Submitted on : Monday, November 29, 2010 - 5:00:11 PM
Last modification on : Thursday, December 10, 2020 - 12:36:48 PM
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  • HAL Id : tel-00541054, version 1


D. Yogeshwaran. Stochastic geometric networks : connectivity and comparison.. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2010. English. ⟨tel-00541054⟩



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