Critical Density for Connectivity in 2D and 3D Wireless Multi-hop Networks

In this paper the authors investigate the critical node density required to ensure that an arbitrary node in a large-scale wireless multi-hop network is connected (via multi-hop path) to infinitely many other nodes with a positive probability. The establishment of a direct connection between any two nodes is independent of connections between other pairs of nodes and its probability satisfies some intuitively reasonable conditions, viz. rotational and translational invariance, non increasing monotonicity, and integral boundedness.