Absolute continuity of heat kernel measure with pinned Wiener measure on loop groups

• 成果类型: Article
• 署名作者: Driver, BK; Srimurthy, VK
• 署名单位: University of California System; University of California San Diego
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1008956690
• 发表日期: 2001
• 页码: 691-723
• 关键词: logarithmic sobolev inequalities; compact riemannian manifold; quasi-invariance theorem; stochastic ising-models; brownian-motion; integration; parts

摘要

Let t > 0, K be a connected compact Lie group equipped with an Ad(K) - invariant inner product on the Lie Algebra of K. Associated to this data are two measures mu (0)(t) and nu (0)(t) on L(K) - the space of continuous loops based at e is an element of K. The measure mu (0)(t) is pinned Wiener measure with variance t while the measure nu (0)(t) is a heat kernel measure on L(K). The measure mu (0)(t) is constructed using a K - valued Brownian motion while the measure nu (0)(t) is constructed using a L(K) - valued Brownian motion. In this paper we show that, v(t)(0) is absolutely continuous with respect to mu (0)(t) and the Radon-Nikodym derivative dv(t)(0)/d mu (0)(t) is bounded.