The scaling limits of the non critical strip wetting model

The strip wetting model is defied by giving a (continuous space) one dimensional random walk S a reward ß each time it hits the strip $R^+ \times [0,a]$ (where a is a given positive parameter), which plays the role of a defect line. We show that this model exhibits a phase transition between a delocalized regime $( \beta > \beta^a_c )$) and a localized one($( \beta > \beta^a_c) $ , where the critical point $ \beta^a_c > 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. Keywords: scaling limits for physical systems, flctuation theory for random walks, Markov renewal theory .