Probability Theory and Related Fields

, Volume 151, Issue 3–4, pp 559–590

A concrete estimate for the weak Poincaré inequality on loop space

Article

DOI: 10.1007/s00440-010-0308-5

Cite this article as:
Chen, X., Li, XM. & Wu, B. Probab. Theory Relat. Fields (2011) 151: 559. doi:10.1007/s00440-010-0308-5

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 sα for any α > 0.

Keywords

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

Mathematics Subject Classification (2000)

60Hxx 58J65 

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Department of MathematicsUniversity of WarwickCoventryUK

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