{
  "id": "0912.0335",
  "version": "v2",
  "published": "2009-12-02T14:50:28.000Z",
  "updated": "2012-10-04T10:29:38.000Z",
  "title": "Invasion percolation on the Poisson-weighted infinite tree",
  "authors": [
    "Louigi Addario-Berry",
    "Simon Griffiths",
    "Ross J. Kang"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/11-AAP761 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2012, Vol. 22, No. 3, 931-970",
  "doi": "10.1214/11-AAP761",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We study invasion percolation on Aldous' Poisson-weighted infinite tree, and derive two distinct Markovian representations of the resulting process. One of these is the $\\sigma\\to\\infty$ limit of a representation discovered by Angel et al. [Ann. Appl. Probab. 36 (2008) 420-466]. We also introduce an exploration process of a randomly weighted Poisson incipient infinite cluster. The dynamics of the new process are much more straightforward to describe than those of invasion percolation, but it turns out that the two processes have extremely similar behavior. Finally, we introduce two new \"stationary\" representations of the Poisson incipient infinite cluster as random graphs on $\\mathbb {Z}$ which are, in particular, factors of a homogeneous Poisson point process on the upper half-plane $\\mathbb {R}\\times[0,\\infty)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-04T10:29:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "poisson-weighted infinite tree",
      "weighted poisson incipient infinite cluster",
      "distinct markovian representations",
      "study invasion percolation",
      "randomly weighted poisson incipient infinite"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.0335A"
    }
  }
}