{
  "id": "1503.04064",
  "version": "v1",
  "published": "2015-03-13T13:45:22.000Z",
  "updated": "2015-03-13T13:45:22.000Z",
  "title": "From Derrida's random energy model to branching random walks: from 1 to 3",
  "authors": [
    "Nicola Kistler",
    "Marius A. Schmidt"
  ],
  "comment": "12 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the extremes of a class of Gaussian fields with in-built hierarchical structure. The number of scales in the underlying trees depends on a parameter alpha in [0,1]: choosing alpha=0 yields the random energy model by Derrida (REM), whereas alpha=1 corresponds to the branching random walk (BRW). When the parameter alpha increases, the level of the maximum of the field decreases smoothly from the REM- to the BRW-value. However, as long as alpha<1 strictly, the limiting extremal process is always Poissonian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-13T13:45:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "82B44",
      "60G70"
    ],
    "keywords": [
      "derridas random energy model",
      "branching random walk",
      "parameter alpha increases",
      "in-built hierarchical structure",
      "limiting extremal process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}