Critical wetting models in (1+1) dimensions

In this talk we will discuss wetting models in (1+1) dimensions pinned to a strip. These polymer models enjoy an interplay between two forces -- local (pinning) and global (entropic repulsion) -- and in many cases a localization-delocalization phase transition holds. The latter known as the wetting transition. In particular, whenever the strip size is fixed and the pinning function is constant and homogeneous in space, phase transition results are available. The standard case, for which the strip size is zero, is completely solved and exhibits a sharp phase transition. In particular, the asymptotic behavior of the system is drastically different in the sub-critical, the super critical and the critical phases. We will focus on the asymptotic of the strip model at criticality when the strip size is shrinking to zero. This is a joint work in progress with Jean-Dominique Deuschel.