{
  "id": "1811.01035",
  "version": "v1",
  "published": "2018-11-02T18:33:38.000Z",
  "updated": "2018-11-02T18:33:38.000Z",
  "title": "Limit theorems for the tagged particle in exclusion processes on regular trees",
  "authors": [
    "Dayue Chen",
    "Peng Chen",
    "Nina Gantert",
    "Dominik Schmid"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider exclusion processes on a rooted $d$-regular tree. We start from a Bernoulli product measure conditioned on having a particle at the root, which we call the tagged particle. For $d\\geq 3$, we show that the tagged particle has positive linear speed and satisfies a central limit theorem. We give an explicit formula for the speed. As a key step in the proof, we first show that the exclusion process \"seen from the tagged particle\" has an ergodic invariant measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-02T18:33:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "tagged particle",
      "exclusion process",
      "regular tree",
      "central limit theorem",
      "ergodic invariant measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}