{
  "annotation_id": "06bb43ed-ab9b-403f-a468-2a258837d355",
  "date_created": "2026-03-02T18:02:50.699000Z",
  "date_modified": "2026-03-02T18:02:50.699000Z",
  "file_hash": "b118d735873d4454260c82863ea3c46e9480b1236f396303ed8f806592d65211",
  "private": false,
  "record": {
    "abstract": "The usual formulas for the correlation functions in orthogonal and symplectic\nmatrix models express them as quaternion determinants. From this representation\none can deduce formulas for spacing probabilities in terms of Fredholm\ndeterminants of matrix-valued kernels. The derivations of the various formulas\nare somewhat involved. In this article we present a direct approach which leads\nimmediately to scalar kernels for unitary ensembles and matrix kernels for the\northogonal and symplectic ensembles, and the representations of the correlation\nfunctions, cluster functions and spacing distributions in terms of them.",
    "arxiv_id": "solv-int/9804004",
    "authors": [
      "Craig A. Tracy",
      "Harold Widom"
    ],
    "categories": [
      "solv-int",
      "math.SP",
      "nlin.SI"
    ],
    "doi": "10.1023/A:1023084324803",
    "journal_ref": "J. Statistical Physics 92 (1998), 809-835.",
    "title": "Correlation Functions, Cluster Functions and Spacing Distributions for   Random Matrices",
    "url": "https://arxiv.org/abs/solv-int/9804004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9d6230bd-b72e-4e23-8bd2-6105e8eea355",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}