Percolation in the secrecy graph: Bounds on the critical probability and impact of power constraints

Secrecy graphs model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the presence of eavesdroppers. In the case of infinite networks, a critical parameter is the maximum density of eavesdroppers that can be accommodated while still guaranteeing an infinite component in the network, i.e., the percolation threshold. We focus on the case where the location of the nodes and the eavesdroppers are given by Poisson point processes, with and without power constraints. We present bounds for different types of percolation, including in-, out - and undirected percolation.