 Percolation two-point connection probability

The two-point percolation two-point connection probability ${\tau }_p(x,y)={\mathbb{P}}_p(x\leftrightarrow y)$ is the probability that two fixed graph vertices belong to the same percolation cluster. On a translation-invariant lattice it depends on their displacement. Restricting the permitted connecting graph paths to a subgraph gives the corresponding confined percolation two-point connection probability. The Harris-FKG inequality implies ${\tau }_p(x,z)\ge {\tau }_p(x,y){\tau }_p(y,z)$.