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A directed path in the vicinity of a hard wall exerts pressure on the wallbecause of loss of entropy. The pressure at a particular point may be estimatedby estimating the loss of entropy if the point is excluded from the path. Inthis paper we determine asymptotic expressions for the pressure on the X-axisin models of adsorbing directed paths in the first quadrant. Our models showthat the pressure vanishes in the limit of long paths in the desorbed phase,but there is a non-zero pressure in the adsorbed phase. We determine asymptoticapproximations of the pressure for finite length Dyck paths and directed paths,as well as for a model of adsorbing staircase polygons with both ends graftedto the X-axis.

The pressure exerted by adsorbing directed lattice paths and staircase polygons