{
  "id": "1507.02265",
  "version": "v1",
  "published": "2015-07-08T19:28:43.000Z",
  "updated": "2015-07-08T19:28:43.000Z",
  "title": "Random planar maps & growth-fragmentations",
  "authors": [
    "Jean Bertoin",
    "Nicolas Curien",
    "Igor Kortchemski"
  ],
  "comment": "42 pages, 8 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We are interested in the cycles obtained by slicing at all heights random Boltzmann triangulations with a simple boundary. We establish a functional invariance principle for the lengths of these cycles, appropriately rescaled, as the size of the boundary grows. The limiting process is described using a self-similar growth-fragmentation process with explicit parameters. To this end, we introduce a branching peeling exploration of Boltzmann triangulations, which allows us to identify a crucial martingale involving the perimeters of cycles at given heights. We also use a recent result concerning self-similar scaling limits of Markov chains on the nonnegative integers. A motivation for this work is to give a new construction of the Brownian map from a growth-fragmentation process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-08T19:28:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random planar maps",
      "heights random boltzmann triangulations",
      "result concerning self-similar scaling limits",
      "self-similar growth-fragmentation process",
      "functional invariance principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150702265B"
    }
  }
}