A concrete estimate for the weak Poincaré inequality on loop space

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Title: A concrete estimate for the weak Poincaré inequality on loop space
Author(s): Chen, X
Li, X-M
Wu, B
Item Type: Journal Article
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.
Publication Date: 12-Jun-2010
Date of Acceptance: 17-May-2010
URI: http://hdl.handle.net/10044/1/54120
DOI: http://dx.doi.org/10.1007/s00440-010-0308-5
ISSN: 1432-2064
Publisher: Springer Verlag
Start Page: 559
End Page: 590
Journal / Book Title: Probability Theory and Related Fields
Volume: 151
Copyright Statement: The final publication is available at Springer via http://dx.doi.org/10.1007/s00440-010-0308-5
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
STATISTICS & PROBABILITY
Brownian bridge measure
Loop space
Orstein-Uhlenbeck operator
Weak Poincare inequality
LOGARITHMIC SOBOLEV INEQUALITIES
COMPACT RIEMANNIAN MANIFOLD
SPECTRAL GAPS
DIFFERENTIAL-CALCULUS
PATH SPACES
COEFFICIENTS
DERIVATIVES
SEMIGROUPS
BEHAVIOR
FORMS
math.PR
math.PR
math.FA
60H07, 46G99
0104 Statistics
Statistics & Probability
Article Number: 3-4
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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