{
  "id": "2107.08854",
  "version": "v1",
  "published": "2021-07-19T13:12:08.000Z",
  "updated": "2021-07-19T13:12:08.000Z",
  "title": "Brownian sheet and time inversion -- From $G$-orbit to $L(G)$-orbit",
  "authors": [
    "Manon Defosseux"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We have proved in a previous paper that a space-time Brownian motion conditioned to remain in a Weyl chamber associated to an affine Kac-Moody Lie algebra is distributed as the radial part process of a Brownian sheet on the compact real form of the underlying finite dimensional Lie algebra, the radial part being defined considering the coadjoint action of a loop group on the dual of a centrally extended loop algebra. We present here a very brief proof of this result based on a time inversion argument and on elementary stochastic differential calculus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-19T13:12:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brownian sheet",
      "affine kac-moody lie algebra",
      "elementary stochastic differential calculus",
      "finite dimensional lie algebra",
      "radial part process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}