{
  "id": "2001.11260",
  "version": "v1",
  "published": "2020-01-30T11:27:40.000Z",
  "updated": "2020-01-30T11:27:40.000Z",
  "title": "Determinantal point processes from symplectic and orthogonal characters and applications",
  "authors": [
    "Dan Betea"
  ],
  "comment": "10 pages; extended abstract version based largely on arXiv:1804.08495 [math-ph]; Theorem 6 is new",
  "categories": [
    "math.PR",
    "math-ph",
    "math.CO",
    "math.MP",
    "math.RT"
  ],
  "abstract": "We show that the symplectic and orthogonal character analogues of Okounkov's Schur measure (on integer partitions) are determinantal, with explicit correlation kernels. We apply this to prove certain Borodin-Okounkov-Gessel-type results concerning Toeplitz+Hankel and Fredholm determinants; a Szeg\\H{o}-type limit theorem; an edge Baik-Deift-Johansson-type asymptotical result for certain symplectic and orthogonal analogues of the poissonized Plancherel measure; and a similar result for actual poissonized Plancherel measures supported on \"almost symmetric\" partitions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-30T11:27:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "determinantal point processes",
      "symplectic",
      "applications",
      "orthogonal character analogues",
      "edge baik-deift-johansson-type asymptotical result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}