Large deviations for symmetric stable processes with Feynman-Kac functionals and its application to pinned polymers (Q2438279)

Let \(\nu\) and \(\mu\) be positive Radon measures on \(\mathbb{R}^d\) which are Green-tight Kato class associated with a symmetric \(\alpha\)-stable process \((X_t,P_x)\) on \(\mathbb{R}^d\), and \(A^\nu_t\) and \(A^\mu_t\) the positive continuous additive functionals under the Revuz correspondence to \(\nu\) and \(\mu\). Let \(P^{\beta u}_{x,t}= (Z^\mu_{x,t})^{-1} \exp\{\beta A^\nu_t\}\), \(\beta> 0\), be the law \(X_t\) weighted by the Feynman-Kac functional \(\exp\{\beta A^\mu_t\}\), where \(Z^\mu_{x,t}\) is a normality constant. Then \(A^\nu_t/t\) obeys the invariant principle under \(P^{\beta,\mu}_{x,t}\).