Characterization of the Critical Density for Percolation in Random Geometric Graphs

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). These analytical lower bounds are the tightest known to date, and reveal a deep underlying relationship between clustering effects and percolation phenomena.