Abstract.
Let K be a simply-connected compact Lie Group equipped with an Ad K -invariant inner product on the Lie Algebra ?, of K. Given this data, there is a well known left invariant “H 1-Riemannian structure” on L(K) (the infinite dimensional group of continuous based loops in K), as well as a heat kernel νT(k 0, ·) associated with the Laplace-Beltrami operator on L(K). Here T > 0, k 0∈L(K), and ν T (k 0, ·) is a certain probability measure on L(K). In this paper we show that ν1(e,·) is equivalent to Pinned Wiener Measure on K on ? s0 ≡<x t : t∈ [0, s 0]> (the σ-algebra generated by truncated loops up to “time”s 0).
Author information
Authors and Affiliations
Additional information
Recevied: 9 September 1999 / Revised version: 13 March 2000 / Published online: 22 November 2000
Rights and permissions
About this article
Cite this article
Srimurthy, V. On the equivalence of measures on loop space. Probab Theory Relat Fields 118, 522–546 (2000). https://doi.org/10.1007/PL00008753
Issue Date:
DOI: https://doi.org/10.1007/PL00008753
Keywords
- Probability Measure
- Heat Kernel
- Loop Space
- Wiener Measure
- Dimensional Group