{
  "id": "1308.4100",
  "version": "v3",
  "published": "2013-08-19T19:07:04.000Z",
  "updated": "2014-06-17T19:18:16.000Z",
  "title": "Markovian loop clusters on the complete graph and coagulation equations",
  "authors": [
    "Sophie Lemaire"
  ],
  "comment": "version 3: 34 pages, 1 figure, results on the phase transition added",
  "categories": [
    "math.PR"
  ],
  "abstract": "Poissonian ensembles of Markov loops on a finite graph define a random graph process in which the addition of a loop can merge more than two connected components. We study Markov loops on the complete graph derived from a simple random walk killed at each step with a constant probability. Using a component exploration procedure, we describe the asymptotic distribution of the connected component size of a vertex at a time proportional to the number of vertices, show that the largest component size undergoes a phase transition and establish the coagulation equations associated to this random graph process.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-17T19:18:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "05C80",
      "60J80",
      "82C31"
    ],
    "keywords": [
      "markovian loop clusters",
      "complete graph",
      "coagulation equations",
      "random graph process",
      "connected component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.4100L"
    }
  }
}