Rectangle crossing in bond percolation
= Rectangle crossing in bond percolation
{title2=$h_p(m,n)$}
For the induced <square lattice> subgraph in $[0,m]\times[0,n]$, $h_p(m,n)$ is the <probability> of an open <graph path> from its left boundary to its right boundary under independent <bond percolation> of density $p$. Width and height count lattice spacings. <Dual bond percolation> exchanges failure with a top-to-bottom dual crossing of dimensions $(m-1)\times(n+1)$, with the usual exterior boundary vertices.