A concrete estimate for the weak Poincaré inequality on loop space

Abstract

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 Poincaré inequality, assuming positivity of the Ricci curvature of the underlying manifold. The order of the rate function is s−α for any α > 0.