{
  "id": "2312.07270",
  "version": "v1",
  "published": "2023-12-12T13:50:49.000Z",
  "updated": "2023-12-12T13:50:49.000Z",
  "title": "On the Sobolev removability of the graph of one-dimensional Brownian motion",
  "authors": [
    "Cillian Doherty",
    "Jason Miller"
  ],
  "comment": "21 pages, 3 figures",
  "categories": [
    "math.PR",
    "math.MG"
  ],
  "abstract": "Suppose that $B$ is a one-dimensional Brownian motion and let $\\Gamma = \\{ (t, B_t) : t \\in [0,1]\\}$ be the graph of $B|_{[0,1]}$. We characterize the Sobolev removability properties of $\\Gamma$ by showing that $\\Gamma$ is almost surely not $W^{1,p}$--removable for all $p \\in [1, \\infty)$ but is almost surely $W^{1,\\infty}$--removable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-12T13:50:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "one-dimensional brownian motion",
      "sobolev removability properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}