A central limit theorem for a one-dimensional polymer measure

Let (S-n)n is an element of N-0 be a random walk on the integers having bounded steps. The self-repellent (resp., self-avoiding) walk is a sequence of transformed path measures which discourage (resp., forbid) self-intersections. This is used as a model for polymers. Previously, we proved a law of large numbers; that is, we showed the convergence of \S-n\/n toward a positive number Theta under the polymer measure. The present paper proves a classical central limit theorem for the self-repellent and self-avoiding walks; that is, we prove the asymptotic normality of (S-n - Theta n)/root n for large n. The proof refines and continues results and techniques developed previously.