{
  "id": "2211.08041",
  "version": "v1",
  "published": "2022-11-15T10:47:02.000Z",
  "updated": "2022-11-15T10:47:02.000Z",
  "title": "The Markov property of local times of Brownian motion indexed by the Brownian tree",
  "authors": [
    "Jean-François Le Gall"
  ],
  "comment": "25 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the model of Brownian motion indexed by the Brownian tree, which has appeared in a variety of different contexts in probability, statistical physics and combinatorics. For this model, the total occupation measure is known to have a continuously differentiable density. Although the density process indexed by nonnegative reals is not Markov, we prove that the pair consisting of the density and its derivative is a time-homogeneous Markov process. We also establish a similar result for the local times of one-dimensional super-Brownian motion. Our methods rely on the excursion theory for Brownian motion indexed by the Brownian tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-15T10:47:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J55",
      "60J65",
      "60J68",
      "60J80"
    ],
    "keywords": [
      "brownian tree",
      "local times",
      "markov property",
      "total occupation measure",
      "one-dimensional super-brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}