Finite size scaling for homogeneous pinning models

Abstract

Pinning models are built from discrete renewal sequences by rewarding (or penalizing) the trajectories according to their number of renewal epochs up to time $N$, and $N$ is then sent to infinity. They are statistical mechanics models to which a lot of attention has been paid both because they are very relevant for applications and because of their {\sl exactly solvable character}, while displaying a non-trivial phase transition (in fact, a localization transition). The order of the transition depends on the tail of the inter-arrival law of the underlying renewal and the transition is continuous when such a tail is sufficiently heavy: this is the case on which we will focus. The main purpose of this work is to give a mathematical treatment of the {\sl finite size scaling limit} of pinning models, namely studying the limit (in law) of the process close to criticality when the system size is proportional to the correlation length.

References in corpus (3)

• Why is the DNA Denaturation Transition First Order?
• A polymer in a multi-interface medium
• Tightness conditions for polymer measures

Cited by in corpus (4)

• Universality for the pinning model in the weak coupling regime
• Polynomial chaos and scaling limits of disordered systems
• Scaling limit of the disordered generalized Poland--Scheraga model for DNA denaturation
• The zeros of the partition function of the pinning model