Analytical Lower Bounds on the Critical Density in Continuum Percolation

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dc.creatorKong, Zhenning
dc.creatorYeh, Edmund M.
dc.date2006-10-25
dc.date2007-04-04
dc.date.accessioned2026-07-07T07:54:58Z
dc.date.available2026-07-07T07:54:58Z
dc.descriptionPercolation theory has become a useful tool for the analysis of large-scale wireless networks. We investigate the fundamental problem of characterizing the critical density $λ_c^{(d)}$ 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 $λ_c^{(d)}$ 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 $λ^{(2)}_c \geq 0.7698...$. For the three-dimensional case, we obtain $λ^{(3)}_c \geq 0.4494...$
dc.identifierhttps://arxiv.org/abs/math/0610751
dc.identifierhttp://arxiv.org/abs/math/0610751
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126813
dc.subjectProbability
dc.subjectMathematical Physics
dc.titleAnalytical Lower Bounds on the Critical Density in Continuum Percolation
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