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On the equivalence of measures on loop space
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  • Published: December 2000

On the equivalence of measures on loop space

  • Vikram K. Srimurthy1 

Probability Theory and Related Fields volume 118, pages 522–546 (2000)Cite this article

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).

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  1. 99 Brookline Street, Cambridge, MA 02139, USA. e-mail: vsrimurt@mediaone.net, , , , , , US

    Vikram K. Srimurthy

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  1. Vikram K. Srimurthy
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Recevied: 9 September 1999 / Revised version: 13 March 2000 / Published online: 22 November 2000

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Srimurthy, V. On the equivalence of measures on loop space. Probab Theory Relat Fields 118, 522–546 (2000). https://doi.org/10.1007/PL00008753

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  • Issue Date: December 2000

  • DOI: https://doi.org/10.1007/PL00008753

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Keywords

  • Probability Measure
  • Heat Kernel
  • Loop Space
  • Wiener Measure
  • Dimensional Group
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