A self-avoiding walk model of random copolymer adsorption

We consider a model of random copolymer adsorption in which a self-avoiding walk interacts with a hypersurface defining a half-space to which the walk is confined. Each vertex of the walk is randomly labelled with areal varia ble which determines the strength of the interaction of that vertex with th e hypersurface. We show that the thermodynamic limit of the quenched averag e free energy exists and is equal to the thermodynamic limit of the free en ergy for almost all fixed labellings, so the system is self-averaging. In a ddition we show that the system exibits a phase transition and we discuss t he connection between the annealed and quenched versions of the problem.