{
  "id": "2403.04108",
  "version": "v1",
  "published": "2024-03-06T23:36:58.000Z",
  "updated": "2024-03-06T23:36:58.000Z",
  "title": "Monotonicity of Recurrence in Random Walks",
  "authors": [
    "Rupert Li",
    "Elchanan Mossel",
    "Benjamin Weiss"
  ],
  "comment": "12 pages, 1 figure",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We consider non-homogeneous random walks on the positive quadrant in two dimensions. In the 1960's the following question was asked: is it true if such a random walk $X$ is recurrent and $Y$ is another random walk that at every point is more likely to go down and more likely to go left than $Y$, then $Y$ is also recurrent? We provide an example showing that the answer is negative. We also show that if either the random walk $X$ or $Y$ is sufficiently homogeneous then the answer is in fact positive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-06T23:36:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10"
    ],
    "keywords": [
      "monotonicity",
      "recurrence",
      "non-homogeneous random walks",
      "positive quadrant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}