LETTER TO THE EDITOR: Staircase polygons, scaling functions and asymmetric compact directed percolation
The scaling function for compact directed percolation on a square lattice is investigated for the asymmetric case where two parameters control the critical behaviour. A simple representation for the area-perimeter generating function for staircase polygons is found, which can be recast as a non-linear functional equation. From this, the exact scaling function is extracted. In the process, the most concise derivations to date are given for the exact low order cluster moments.