{
  "annotation_id": "393481e2-5968-4ddf-ad38-90d0ebbcd691",
  "date_created": "2026-03-02T18:01:27.604000Z",
  "date_modified": "2026-03-02T18:01:27.604000Z",
  "file_hash": "ec1ea266fb5ccd113f9f118578b33c184b6c0c628032a1d25becc0c63764159f",
  "private": false,
  "record": {
    "abstract": "Using a probabilistic interpretation of the Burau representation of the braid\ngroup offered by Vaughan Jones, we generalize the Burau representation to a\nrepresentation of the semigroup of string links. This representation is\ndetermined by a linear system, and is dominated by finite type string link\ninvariants. For positive string links, the representation matrix can be\ninterpreted as the transition matrix of a Markov process. For positive\nnon-separable links, we show that all states are persistent. (This is an\nextensively revised version of the first author\u0027s original paper titled \"Burau\nrepresentation and random walk on knots\".)",
    "arxiv_id": "q-alg/9605023",
    "authors": [
      "Xiao-Song Lin",
      "Feng Tian",
      "Zhenghan Wang"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Burau representation and random walk on string links",
    "url": "https://arxiv.org/abs/q-alg/9605023"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "782707c0-6469-4401-b7bd-ce279e8ee9b7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}