The strip wetting model is defined by giving a (continuous space) one dimensionnal random walk $S$ a reward $\gb$ each time it hits the strip $\R^{ +} \times [0,a]$ (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 ($\gb < \gb_{ c}^{ a}$) and a localized one ($\gb > \gb_{ c}^{ a}$), where the critical point $\gb_{ c}^{ a} > 0$ 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.
Categories: math.PR