  We consider a model for a polymer interacting with an attractive wall through
a random sequence of charges. We focus on the so-called diluted limit, when the
charges are very rare but have strong intensity. In this regime, we determine
the quenched critical point of the model, showing that it is different from the
annealed one. The proof is based on a rigorous renormalization procedure.
Applications of our results to the problem of a copolymer near a selective
interface are discussed.
