{
  "id": "1312.1137",
  "version": "v1",
  "published": "2013-12-04T12:33:03.000Z",
  "updated": "2013-12-04T12:33:03.000Z",
  "title": "Extremal Aging For Trap Models",
  "authors": [
    "Onur Gün"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In the seminal work [5], Ben Arous and \\v{C}ern\\'y give a general characterization of aging for trap models in terms of $\\alpha$-stable subordinators with $\\alpha \\in (0,1)$. Some of the important examples that fall into this universality class are Random Hopping Time (RHT) dynamics of Random Energy Model (REM) and $p$-spin models observed on exponential time scales. In this paper, we explain a different aging mechanism in terms of {\\it extremal processes} that can be seen as the extension of $\\alpha$-stable aging to the case $\\alpha=0$. We apply this mechanism to the RHT dynamics of the REM for a wide range of temperature and time scales. The other examples that exhibit extremal aging include the Sherrington Kirkpatrick (SK) model and $p$-spin models [6, 9], and biased random walk on critical Galton-Watson trees conditioned to survive [11].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-04T12:33:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C44",
      "82D30",
      "60G70"
    ],
    "keywords": [
      "trap models",
      "extremal aging",
      "spin models",
      "random energy model",
      "exponential time scales"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.1137G"
    }
  }
}