On directed compact percolation near a damp wall

A percolation probability for directed, compact percolation near a damp wall, which interpolates between the previously examined cases, is derived exactly. We find that the critical exponent beta = 2 in common with the dry wall, rather than the value previously found in the wet wall and bulk cases. The solution is found via a mapping to a particular model of directed walks. We evaluate the exact generating function for this walk model which is also related to the ASEP model of traffic flow. We compare the underlying mathematical structure of the various cases previously considered and this one by reviewing the common framework of solution via the mapping to different directed walk models.