LARGE DEVIATIONS FOR SYMMETRIC STABLE PROCESSES WITH FEYNMAN-KAC FUNCTIONALS AND ITS APPLICATION TO PINNED POLYMERS

Let v and mu be positive Radon measures on R-d in Green-tight Kato class associated with a symmetric alpha-stable process (X-t, P-x) on R-d, and A(t)(v) and A(t)(mu) the positive continuous additive functionals under the Revuz correspondence to v and mu. For a non-negative beta, let P-x,t(beta mu) be the law X-t weighted by the Feynman-Kac functional exp(beta A(t)(mu)), i.e., P-x,t(mu) = (Z(x,t)(mu))(-1) exp(beta A(t)(mu))P-x, where Z(x,t)(mu) is a normalizing constant. We show that A(t)(v)/t obeys the large deviation principle under P-x,t(beta mu). We apply it to a polymer model to identify the critical value beta(cr) such that the polymer is pinned under the law P-x,t(beta mu) if and only if beta is greater than beta(cr). The value beta(cr) is characterized by the rate function.