  We consider a directed random walk model of a random heterogeneous polymer in
the proximity of an interface separating two selective solvents. This model
exhibits a localization/delocalization transition. A positive value of the free
energy corresponds to the localized regime and strong results on the polymer
path behavior are known in this case. We focus on the interior of the
delocalized phase, which is characterized by the free energy equal to zero, and
we show in particular that in this regime there are O(log N) monomers in the
unfavorable solvent (N is the length of the polymer). The previously known
result was o(N). Our approach is based on concentration bounds on suitably
restricted partition functions. The same idea allows also to interpolate
between different types of disorder in the weak coupling limit. In this way we
show the universal nature of this limit, previously considered only for binary
disorder.
