Some rigorous results on semiflexible polymers, I: Free and confined polymers

We introduce a class of models of semiflexible polymers. The latter are characterized by a strong rigidity, the correlation length associated with the gradient-gradient correlations, called the persistence length, being of the same order as the polymer length. We determine the macroscopic scaling limit, from which we deduce bounds on the free energy of a polymer confined inside a narrow tube.