{
  "id": "0805.0480",
  "version": "v1",
  "published": "2008-05-05T08:19:12.000Z",
  "updated": "2008-05-05T08:19:12.000Z",
  "title": "Spectral gap for the interchange process in a box",
  "authors": [
    "Ben Morris"
  ],
  "comment": "8 pages. I learned after completing a draft of this paper that its main result had recently been obtained by Starr and Conomos",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that the spectral gap for the interchange process (and the symmetric exclusion process) in a $d$-dimensional box of side length $L$ is asymptotic to $\\pi^2/L^2$. This gives more evidence in favor of Aldous's conjecture that in any graph the spectral gap for the interchange process is the same as the spectral gap for a corresponding continuous-time random walk. Our proof uses a technique that is similar to that used by Handjani and Jungreis, who proved that Aldous's conjecture holds when the graph is a tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-05T08:19:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C22",
      "60K35"
    ],
    "keywords": [
      "spectral gap",
      "interchange process",
      "aldouss conjecture holds",
      "corresponding continuous-time random walk",
      "symmetric exclusion process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.0480M"
    }
  }
}