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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(d)</sup> 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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(d)</sup> . These analytical lower bounds are the tightest known to date, and reveal a deep underlying relationship between clustering effects and percolation phenomena.
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