A concrete estimate for the weak Poincaré inequality on loop space
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- Chen, X., Li, XM. & Wu, B. Probab. Theory Relat. Fields (2011) 151: 559. doi:10.1007/s00440-010-0308-5
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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.