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.
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X.-M. Li’s research was supported by the EPSRC (EP/E058124/1).
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Chen, X., Li, XM. & Wu, B. A concrete estimate for the weak Poincaré inequality on loop space. Probab. Theory Relat. Fields 151, 559–590 (2011). https://doi.org/10.1007/s00440-010-0308-5
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DOI: https://doi.org/10.1007/s00440-010-0308-5
Keywords
- Brownian bridge measure
- Loop space
- Orstein–Uhlenbeck operator
- Weak Poincaré inequality
Mathematics Subject Classification (2000)
- 60Hxx
- 58J65