The scaling limits of the non critical strip wetting model

The strip wetting model is defined by giving a (continuous space) one dimensional random walk S a reward β each time it hits the strip R+×[0,a] (where a is a positive parameter), which plays the role of a defect line. We show that this model exhibits a phase transition between a delocalized regime (β<βca) and a localized one (β>βca), where the critical point βca>0 depends on S and on a. In this paper we give a precise pathwise description of the transition, extracting the full scaling limits of the model. Our approach is based on Markov renewal theory.