{
  "id": "1102.4937",
  "version": "v3",
  "published": "2011-02-24T09:25:23.000Z",
  "updated": "2012-05-01T08:17:18.000Z",
  "title": "Brownian Motions on Metric Graphs",
  "authors": [
    "Vadim Kostrykin",
    "Jürgen Potthoff",
    "Robert Schrader"
  ],
  "comment": "43 pages, 7 figures. 2nd revision of our article 1102.4937: The introduction has been modified, several references were added. This article will appear in the special issue of Journal of Mathematical Physics celebrating Elliott Lieb's 80th birthday",
  "categories": [
    "math.PR"
  ],
  "abstract": "Brownian motions on a metric graph are defined. Their generators are characterized as Laplace operators subject to Wentzell boundary at every vertex. Conversely, given a set of Wentzell boundary conditions at the vertices of a metric graph, a Brownian motion is constructed pathwise on this graph so that its generator satisfies the given boundary conditions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-05-01T08:17:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60J45",
      "60H99",
      "58J65",
      "35K05",
      "05C99",
      "05.40.Jc",
      "02.10.Ox",
      "02.30.Jr",
      "02.30.Tb"
    ],
    "keywords": [
      "metric graph",
      "brownian motion",
      "wentzell boundary conditions",
      "laplace operators subject",
      "generator satisfies"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.4714661",
      "journal": "Journal of Mathematical Physics",
      "year": 2012,
      "month": "Sep",
      "volume": 53,
      "number": 9,
      "pages": 5206
    },
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JMP....53i5206K"
    }
  }
}