{
  "id": "1410.0807",
  "version": "v1",
  "published": "2014-10-03T10:19:39.000Z",
  "updated": "2014-10-03T10:19:39.000Z",
  "title": "Functional limit theorems for the Bouchaud trap model with slowly-varying traps",
  "authors": [
    "David Croydon",
    "Stephen Muirhead"
  ],
  "comment": "28 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the Bouchaud trap model on the integers in the case that the trap distribution has a slowly-varying tail at infinity. Our main result is a functional limit theorem for the model under the annealed law, analogous to the functional limit theorems previously established in the literature in the case of integrable or regularly-varying trap distribution. Reflecting the fact that the clock process is dominated in the limit by the contribution from the deepest-visited trap, the limit process for the model is a spatially-subordinated Brownian motion whose associated clock process is an extremal process. We identify this process as the $\\alpha \\to 0$ scaling limit of the FIN diffusion with parameter $\\alpha$. Additionally, we study a natural `transparent' generalisation of the Bouchaud trap model with slowly-varying trap distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-03T10:19:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bouchaud trap model",
      "functional limit theorem",
      "clock process",
      "main result",
      "spatially-subordinated brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.0807C"
    }
  }
}