Polymer pinning at an interface

We consider a (1+1)-dimensional hydrophobic homopolymer, in interaction with an oil–water interface. In , the interface is modelled by the x axis, the oil is above, the water is below, and the polymer configurations are given by a simple random walk (Si)i=0. The hydrophobicity of each monomer tends to delocalize the polymer in the upper half-plane, through a reward h>0 for each monomer in the oil and a penalty -h