{
  "id": "2104.11477",
  "version": "v1",
  "published": "2021-04-23T08:48:09.000Z",
  "updated": "2021-04-23T08:48:09.000Z",
  "title": "Ratio limits and Martin boundary",
  "authors": [
    "Wolfgang Woess"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider an irreducible Markov chain which satisfies a ratio limit theorem, and let $\\rho$ be the spectral radius of the chain. We investigate the relation of the the $\\rho\\,$-Martin boundary with the boundary induced by the $\\rho\\,$-harmonic kernel which appears in the ratio limit. Special emphasis is on random walks on non-amenable groups, specifically, free groups and hyperbolic groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-23T08:48:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "martin boundary",
      "ratio limit theorem",
      "random walks",
      "free groups",
      "irreducible markov chain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}