{
  "id": "1502.04535",
  "version": "v1",
  "published": "2015-02-16T13:52:46.000Z",
  "updated": "2015-02-16T13:52:46.000Z",
  "title": "Aging of the Metropolis dynamics on the Random Energy Model",
  "authors": [
    "Jiří Černý",
    "Tobias Wassmer"
  ],
  "comment": "37 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the Metropolis dynamics of the simplest mean-field spin glass model, the Random Energy Model. We show that this dynamics exhibits aging by showing that the properly rescaled time change process between the Metropolis dynamics and a suitably chosen `fast' Markov chain converges in distribution to a stable subordinator. The rescaling might depend on the realization of the environment, but we show that its exponential growth rate is deterministic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-16T13:52:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random energy model",
      "metropolis dynamics",
      "rescaled time change process",
      "simplest mean-field spin glass model",
      "exponential growth rate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}