{
  "annotation_id": "4f95564f-9f7a-41d6-87eb-ba32e0a02066",
  "date_created": "2026-03-02T18:01:10.922000Z",
  "date_modified": "2026-03-02T18:01:10.922000Z",
  "file_hash": "f6318da4a8b3b6bcdabe08bc14568bdb3547306b8ed0ecd31d1c8446a70e92d3",
  "private": false,
  "record": {
    "abstract": "A new object of the probability theory, the two-sided chain of symbols\n(introduced in Ref. arXiv:physics/0306170) is used to study isotropy properties\nof binary multi-step Markov chains with the long-range correlations.\nEstablished statistical correspondence between the Markov chains and certain\ntwo-sided sequences allows us to prove the isotropy properties of three classes\nof the Markov chains. One of them is the important class of weakly correlated\nadditive Markov chains, which turned out to be equivalent to the additive\ntwo-sided sequences.",
    "arxiv_id": "physics/0607225",
    "authors": [
      "S. S. Apostolov",
      "Z. A. Mayzelis",
      "O. V. Usatenko",
      "V. A. Yampol\u0027skii"
    ],
    "categories": [
      "physics.data-an",
      "physics.class-ph"
    ],
    "doi": "10.1016/j.physa.2006.10.069",
    "title": "Isotropy Properties of the Multi-Step Markov Symbolic Sequences",
    "url": "https://arxiv.org/abs/physics/0607225"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "afc65e1c-09df-4680-a79d-f74741933174",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}