{
  "id": "1510.06191",
  "version": "v1",
  "published": "2015-10-21T10:18:36.000Z",
  "updated": "2015-10-21T10:18:36.000Z",
  "title": "Quenched localisation in the Bouchaud trap model with slowly varying traps",
  "authors": [
    "David Croydon",
    "Stephen Muirhead"
  ],
  "comment": "36 pages, 4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the quenched localisation of the Bouchaud trap model on the positive integers in the case that the trap distribution has a slowly varying tail at infinity. Our main result is that for each $N \\in \\{2, 3, \\ldots\\}$ there exists a slowly varying tail such that quenched localisation occurs on exactly $N$ sites. As far as we are aware, this is the first example of a model in which the exact number of localisation sites are able to be `tuned' according to the model parameters. Key intuition for this result is provided by an observation about the sum-max ratio for sequences of independent and identically distributed random variables with a slowly varying distributional tail, which is of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-21T10:18:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bouchaud trap model",
      "quenched localisation",
      "slowly varying traps",
      "slowly varying tail",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151006191C"
    }
  }
}