{
  "id": "2003.01684",
  "version": "v1",
  "published": "2020-03-03T18:10:38.000Z",
  "updated": "2020-03-03T18:10:38.000Z",
  "title": "Cutpoints of non-homogeneous random walks",
  "authors": [
    "Chak Hei Lo",
    "Mikhail V. Menshikov",
    "Andrew R. Wade"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give conditions under which near-critical stochastic processes on the half-line have infinitely many or finitely many cutpoints, generalizing existing results on nearest-neighbour random walks to adapted processes with bounded increments satisfying appropriate conditional increment moments conditions. We apply one of these results to deduce that a class of transient zero-drift Markov chains in $\\mathbb{R}^d$, $d \\geq 2$, possess infinitely many separating annuli, generalizing previous results on spatially homogeneous random walks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-03T18:10:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J05",
      "60J10",
      "60G50"
    ],
    "keywords": [
      "non-homogeneous random walks",
      "increments satisfying appropriate conditional",
      "appropriate conditional increment moments conditions",
      "satisfying appropriate conditional increment moments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}