Disordered pinning models: beyond annealed bounds

I will discuss models of directed d-dimensional polymers interacting with a 1-dimensional defect (e.g. (1+1)-dimensional wetting models) in presence of quenched randomness. These may be seen as renewal processes perturbed by disorder. These models undergo a localization/delocalization phase transition. I will discuss heuristic predictions and rigorous results concerning the relation between the (quenched) critical point and critical exponents to the critical point and critical exponents of the corresponding (easy) annealed model. In particular, I will present a simple method, based on the estimation of non-integer moments of the partition function, whici allows to prove that quenched and annealed critical points differ in some situations, and to find the asymptotics of the critical point for large disorder. In particular, in the large disorder limit this makes rigorous some heuristic renormalization-group predictions made previously in the physics literature. If time allows, I will also present related recent results (obtained in collaboration with Giambattista Giacomin and Hubert Lacoin) about a hierarchical version of these models.