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 $\lambda_c^{(d)}$ 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 $\lambda_c^{(d)}$ 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 $\lambda^{(2)}_c \geq 0.7698…$. For the
three-dimensional case, we obtain $\lambda^{(3)}_c \geq 0.4494…$