RSW reflection extension lemma (source code)

= RSW reflection extension lemma
{c}

For independent <bond percolation> on the <square lattice> at $p=1/2$, square crossing <probabilities> bounded below by self-duality extend to a uniform positive bound for rectangles of aspect ratio $3/2$. Expose an extremal vertical square crossing, reflect its geometry, and attach it to an exterior side through an unexposed independent region. Reflection symmetry bounds the attachment <probability> below. Two attachments and a horizontal square crossing join by the <Harris-FKG inequality>. Overlapping rectangles and transverse overlap-square crossings then give all fixed aspect ratios. Reflecting a geometrical <graph path> does not require its reflected <edges> to be open.