Uniform RSW crossing estimate

ID: uniform-rsw-crossing-estimate

For independent bond percolation on the square lattice, a positive uniform lower bound for square crossings implies a positive uniform lower bound for rectangle crossings of every fixed aspect ratio . The RSW reflection extension lemma first extends a square to aspect ratio . Overlapping rectangles and transverse overlap-square crossings then glue using the Harris-FKG inequality. The required constant depends on and , not on scale. At a self-dual parameter, dual crossings also give a uniform upper bound below one.

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