{
  "annotation_id": "c3c18405-2346-4aee-b219-f2cc9c7b31b3",
  "date_created": "2026-02-17T05:53:26.423000Z",
  "date_modified": "2026-02-17T05:53:26.423000Z",
  "file_hash": "0ce404a300c89519c49b7f748fdda6c6bbce43e38a7c3cd68c478c6f40bfa5b2",
  "private": false,
  "record": {
    "abstract": "We consider the problem of locating the source (starting vertex) of a simple random walk, given a snapshot of the set of edges (or vertices) visited in the first $n$ steps. Considering lattices $\\mathbb{Z}^d$, in dimensions $d \\geq 5$, we show that the source can be identified (a) with probability bounded away from $0$ using one guess, and (b) with probability arbitrarily close to $1$ using a constant number of guesses. On the other hand, for dimensions $d \\leq 2$, we show that one cannot locate the source with positive constant probability. Our arguments apply more generally to strongly transient and recurrent simple random walks on vertex-transitive graphs.",
    "arxiv_id": "2601.10624",
    "authors": [
      "Ritesh Goenka",
      "Peter Keevash",
      "Tomasz Przyby\u0142owski"
    ],
    "categories": [
      "math.PR",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Source localisation in simple random walks",
    "url": "https://arxiv.org/abs/2601.10624",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "951da582-0852-47a0-832d-d696c68e6988",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}