We consider a quenched-disordered heteropolymer, consisting of hydrophobic
and hydrophylic monomers, in the vicinity of an oil-water interface. The he
teropolymer is modeled by a directed simple random walk (i, S-i)(i is an el
ement of N) on N x Z with an interaction given by the Hamiltonians H-n(omeg
a)(S) = lambda Sigma(i=1)(n)(omega(i) + h)Sign(S-i) (n is an element of N).
Here, lambda and h are parameters and (omega(i))(i is an element of N) are
i.i.d. ii-valued random variables. The sign(S-i)= +/-1 indicates whether t
he ith monomer is above or below the interface, the omega(i) = +/-1 indicat
es whether the ith monomer is hydrophobic or hydrophylic. It was shown by B
olthausen and den Hollander that the free energy exhibits a localization-de
localization phase transition at a curve in the (lambda, h)-plane. In the p
resent paper we show that the free-energy localization concept is equivalen
t to pathwise localization. In particular, we prove that free-energy locali
zation implies exponential tightness of the polymer excursions away from th
e interface, strictly positive density of intersections with the interface
and convergence of ergodic averages along the polymer. We include an argume
nt due to G. Giacomin, showing that free-energy delocalization implies that
there is pathwise delocalization in a certain weak sense.