Percolation two-point connection probability (source code)

= Percolation two-point connection probability
{title2=$\tau_p(x,y)=\mathbb P_p(x\leftrightarrow y)$}

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 $\tau_p(x,z)\geq\tau_p(x,y)\tau_p(y,z)$.