{
  "id": "2506.16259",
  "version": "v1",
  "published": "2025-06-19T12:23:16.000Z",
  "updated": "2025-06-19T12:23:16.000Z",
  "title": "Two-dimensional Rademacher walk",
  "authors": [
    "Satyaki Bhattacharya",
    "Stanislav Volkov"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a generalisation of the one-dimensional Rademacher random walk introduced in Bhattacharya and Volkov (2023) to $\\mathbb{Z}^2$ (for $d\\ge 3$, the Rademacher random walk is always transient, as follows from Theorem 8.8 in Englander and Volkov (2025)). This walk is defined as the sum of a sequence of independent steps, where each step goes in one of the four possible directions with equal probability, and the size of the $n$th step is $a_n$ where $\\{a_n\\}$ is a given sequence of positive integers. We establish some general conditions under which the walk is recurrent, respectively, transient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-06-19T12:23:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60J10"
    ],
    "keywords": [
      "two-dimensional rademacher walk",
      "one-dimensional rademacher random walk",
      "general conditions",
      "independent steps",
      "equal probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}