Analytical Lower Bounds on the Critical Density in Continuum Percolation

Zhenning Kong; Edmund M. Yeh

1st International ICST Workshop on Spatial Stochastic Models for Wireless Networks

Research Article

Analytical Lower Bounds on the Critical Density in Continuum Percolation

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.1109/WIOPT.2007.4480080,
    author={Zhenning Kong and Edmund M. Yeh},
    title={Analytical Lower Bounds on the Critical Density in Continuum Percolation},
    proceedings={1st International ICST Workshop on Spatial Stochastic Models for Wireless Networks},
    publisher={IEEE},
    proceedings_a={SPASWIN},
    year={2008},
    month={3},
    keywords={Analytical models  Bonding  Decoding  Large-scale systems  Lattices  Mathematical model  Probability density function  Random variables  Solid modeling  Wireless networks},
    doi={10.1109/WIOPT.2007.4480080}
}

Zhenning Kong
Edmund M. Yeh
Year: 2008
Analytical Lower Bounds on the Critical Density in Continuum Percolation
SPASWIN
IEEE
DOI: 10.1109/WIOPT.2007.4480080

Zhenning Kong¹^,*, Edmund M. Yeh¹^,*

1: Department of Electrical Engineering Yale University New Haven, CT 06520, USA

*Contact email: zhenning.kong@yale.edu, edmund.yeh@yale.edu

Abstract

Percolation theory has become a useful tool for the analysis of large-scale wireless networks. We investigate the fundamental problem of characterizing the critical density lambdac (d) for d-dimensional Poisson random geometric graphs in continuum percolation theory. By using a probabilistic analysis which incorporates the clustering effect in random geometric graphs, we develop a new class of analytical lower bounds for the critical density lambdac (d) in d-dimensional Poisson random geometric graphs. The lower bounds are the tightest known to date. In particular, for the two-dimensional case, the analytical lower bound is improved to lambdac (2) ges 0.7698. For the three-dimensional case, we obtain lambdac (3) ges 0.4494.

Keywords: Analytical models Bonding Decoding Large-scale systems Lattices Mathematical model Probability density function Random variables Solid modeling Wireless networks

Published: 2008-03-31
Publisher: IEEE
Modified: 2011-07-28

: http://dx.doi.org/10.1109/WIOPT.2007.4480080