A concrete estimate for the weak Poincaré inequality on loop space

The aim of the paper is to study the pinned Wiener measure on the loop space over a simply connected compact Riemannian manifold together with a Hilbert space structure and the Ornstein-Uhlenbeck operator d*d. We give a concrete estimate for the weak Poincar, inequality, assuming positivity of the Ricci curvature of the underlying manifold. The order of the rate function is s (-alpha) for any alpha > 0