{
  "annotation_id": "97b41d0d-a4ae-4a6a-afbb-cb06889901f1",
  "date_created": "2026-03-02T18:02:51.206000Z",
  "date_modified": "2026-03-02T18:02:51.206000Z",
  "file_hash": "a940349b1940e8b7c8e102c5504ccd72d0bb7ada419e1c363b54fc012a34a7dc",
  "private": false,
  "record": {
    "abstract": "What is the connection of random matrices with integrable systems? Is this\nconnection really useful? Introducing apprpriate times in the distribution of\nthe ensemble of matrices, one shows that the corresponding distribution of the\neigenvalues satisfies the KP-equation, the 1-Toda lattice or the 2-Toda\nlattice, depending on the original distribution. The probability distribution\nalso satisfies Virasoro type constraints, which contain a time-part and a\nboundary-part. These equations taken together lead to a system of PDE\u0027s for the\ndistribution of the spectrum in terms of the boundary of the set, under\nconsideration.",
    "arxiv_id": "solv-int/9706009",
    "authors": [
      "Pierre van Moerbeke"
    ],
    "categories": [
      "solv-int",
      "nlin.SI"
    ],
    "journal_ref": "Group21, Physical applications and Mathematical aspects of\n  Geometry, Groups and Algebras, Vol II, 835--852, Eds.: Doebner, Scherer,\n  Schulte, World Scientific, Singapore, 1997",
    "title": "The spectrum of random matrices and integrable systems",
    "url": "https://arxiv.org/abs/solv-int/9706009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fd888618-736c-4d09-97d1-c23c21b5d1c2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}