  To study the localization of random heteropolymers at an interface separating
two selective solvents within the model of Garel, Huse, Leibler and Orland,
Europhys. Lett. {\bf 8} 9 (1989), we propose an approach based on a
disorder-dependent real space renormalization procedure. This approach allows
to recover that a chain with a symmetric distribution in
hydrophobic/hydrophilic components is localized at any temperature in the
thermodynamic limit, whereas a dissymmetric distribution in
hydrophobic/hydrophilic components leads to a delocalization phase transition.
It yields in addition explicit expressions for the thermodynamic quantities as
well as a very detailed description of the statistical properties of the
behaviors of the heteropolymers in the high temperature limit. For the case of
a small dissymmetry in hydrophobic/hydrophilic components, the renormalization
approach yields explicit predictions for the delocalization transition
temperature and for the critical behaviors of various quantities : in
particular, the free energy presents an essential singularity at the
transition, the typical length of blobs in the preferred solvent diverges with
an essential singularity, whereas the typical length of blobs in the other
solvent diverges algebraically. Finite-size properties are also characterized
in details for both cases. In particular, we give the probability distribution
of the delocalization temperature for the ensemble of chains of finite (large)
length $L$. Finally, we discuss the non-equilibrium dynamics at temperature $T$
starting from a zero-temperature initial condition.
