{
  "annotation_id": "da92c1e1-b7e3-4e4d-b199-b34a34b51055",
  "date_created": "2026-03-02T18:00:42.473000Z",
  "date_modified": "2026-03-02T18:00:42.473000Z",
  "file_hash": "7d491d6969bc15429d377b3bf6cf7a87a03e03cabb197c98e4c9e75c89dccf38",
  "private": false,
  "record": {
    "abstract": "A theory of systems with long-range correlations based on the consideration\nof binary N-step Markov chains is developed. In our model, the conditional\nprobability that the i-th symbol in the chain equals zero (or unity) is a\nlinear function of the number of unities among the preceding N symbols. The\nmodel allows exact analytical treatment. The correlation and distribution\nfunctions as well as the variance of number of symbols in the words of\narbitrary length L are obtained analytically and numerically. A self-similarity\nof the studied stochastic process is revealed and the similarity transformation\nof the chain parameters is presented. The diffusion equation governing the\ndistribution function of the L-words is explored. If the persistent\ncorrelations are not extremely strong, the distribution function is shown to be\nthe Gaussian with the variance being nonlinearly dependent on L. The\napplicability of the developed theory to the coarse-grained written and DNA\ntexts is discussed.",
    "arxiv_id": "physics/0211053",
    "authors": [
      "O. V. Usatenko",
      "V. A. Yampol\u0027skii"
    ],
    "categories": [
      "physics.data-an",
      "physics.class-ph"
    ],
    "title": "Binary N-Step Markov Chain as an Exactly Solvable Model of Long-Range   Correlated Systems",
    "url": "https://arxiv.org/abs/physics/0211053"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "56d12ae0-2cab-4a2a-a6a1-4d5d56a20377",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}