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A concrete estimate for the weak Poincaré inequality on loop space
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  • Published: 12 June 2010

A concrete estimate for the weak Poincaré inequality on loop space

  • Xin Chen1,
  • Xue-Mei Li2 &
  • Bo Wu1 

Probability Theory and Related Fields volume 151, pages 559–590 (2011)Cite this article

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  • 6 Citations

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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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Author information

Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Xin Chen & Bo Wu

  2. Department of Mathematics, University of Warwick, Coventry, CV4 7AL, UK

    Xue-Mei Li

Authors
  1. Xin Chen
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  2. Xue-Mei Li
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  3. Bo Wu
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Corresponding author

Correspondence to Xin Chen.

Additional information

X.-M. Li’s research was supported by the EPSRC (EP/E058124/1).

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Cite this article

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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  • Received: 03 November 2009

  • Revised: 17 May 2010

  • Published: 12 June 2010

  • Issue Date: December 2011

  • DOI: https://doi.org/10.1007/s00440-010-0308-5

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Keywords

  • Brownian bridge measure
  • Loop space
  • Orstein–Uhlenbeck operator
  • Weak Poincaré inequality

Mathematics Subject Classification (2000)

  • 60Hxx
  • 58J65
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