{
  "annotation_id": "01631945-57b9-4a73-a35b-f165c1b23c41",
  "date_created": "2026-03-02T18:02:50.754000Z",
  "date_modified": "2026-03-02T18:02:50.754000Z",
  "file_hash": "f6ea383a975a4a7534a611aaa5bc23cec783c857dbbe438102dd85076eaa4780",
  "private": false,
  "record": {
    "abstract": "Consider a symmetric (finite) matrix ensemble, with a certain probability\ndistribution. What is the probability that the spectrum belongs to a certain\ninterval or union of intervals on the real line? In this paper, we show that,\nupon introducing an appropriate time parameter, this probability is intimately\nrelated to Pfaffians, which as a vector satisfy the so-called Pfaff lattice.\nThe latter is a particular reduction of the 2d-Toda lattice. In particular,\nthey satisfy a KP-like equation, but with a right hand side, depending on\nnearest neighbors. They also satisfy Virasoro constraints, which combined with\nthe KP-like equation lead to inductive equations for the probabilities.",
    "arxiv_id": "solv-int/9903009",
    "authors": [
      "M. Adler",
      "P. van Moerbeke"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "title": "Symmetric random matrices and the Pfaff lattice",
    "url": "https://arxiv.org/abs/solv-int/9903009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6f8d921b-818b-46c2-82bb-ba4176f1ab46",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}