{
  "annotation_id": "17a991e7-c45d-4dba-af3b-374bd8369e31",
  "date_created": "2026-03-02T18:02:03.630000Z",
  "date_modified": "2026-03-02T18:02:03.630000Z",
  "file_hash": "78317b8d21121d3bfdf37ac0e70c4085db3b005ef922a5b5008a7711d57de488",
  "private": false,
  "record": {
    "abstract": "We formulate and prove a general weak limit theorem for quantum random walks\nin one and more dimensions. With $X_n$ denoting position at time $n$, we show\nthat $X_n/n$ converges weakly as $n \\to \\infty$ to a certain distribution which\nis absolutely continuous and of bounded support. The proof is rigorous and\nmakes use of Fourier transform methods. This approach simplifies and extends\ncertain preceding derivations valid in one dimension that make use of\ncombinatorial and path integral methods.",
    "arxiv_id": "quant-ph/0309135",
    "authors": [
      "Geoffrey Grimmett",
      "Svante Janson",
      "Petra Scudo"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "doi": "10.1103/PhysRevE.69.026119",
    "title": "Weak limits for quantum random walks",
    "url": "https://arxiv.org/abs/quant-ph/0309135"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1877c517-56e0-4844-842a-e4d0f1e193eb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}