{
  "id": "1606.02703",
  "version": "v1",
  "published": "2016-06-08T19:52:12.000Z",
  "updated": "2016-06-08T19:52:12.000Z",
  "title": "Mixing time for exclusion and interchange processes on hypergraphs",
  "authors": [
    "Stephen B. Connor",
    "Richard Pymar"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We introduce a natural extension of the exclusion process to hypergraphs and prove an upper bound for its mixing time. In particular we show the existence of a constant $C$ such that for any connected hypergraph $G$ within some class (which includes regular hypergraphs), the $\\varepsilon$-mixing time of the exclusion process on $G$ with any feasible number of particles can be upper-bounded by $CT_{\\text{EX}(2,G)}\\log(|V|/\\varepsilon)$, where $|V|$ is the number of vertices in $G$ and $T_{\\text{EX}(2,G)}$ is the 1/4-mixing time of the corresponding exclusion process with two particles. We also obtain a similar result for the interchange process provided the number of particles is at most $|V|/2$. The proofs involve an adaptation of the chameleon process, a technical tool invented by Morris and developed by Oliveira for studying the exclusion process on a graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-08T19:52:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "60K35",
      "82C22"
    ],
    "keywords": [
      "mixing time",
      "interchange process",
      "upper bound",
      "corresponding exclusion process",
      "regular hypergraphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}