A concrete estimate for the weak Poincar, inequality on loop space

• 成果类型: Article
• 署名作者: Chen, Xin; Li, Xue-Mei; Wu, Bo
• 署名单位: University of Warwick; University of Warwick
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-010-0308-5
• 发表日期: 2011
• 页码: 559-590
• 关键词: logarithmic sobolev inequalities; differential-calculus; spectral gaps; path; BEHAVIOR

摘要

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 Poincar, inequality, assuming positivity of the Ricci curvature of the underlying manifold. The order of the rate function is s (-alpha) for any alpha > 0.