{
  "id": "1701.02296",
  "version": "v1",
  "published": "2017-01-09T18:43:19.000Z",
  "updated": "2017-01-09T18:43:19.000Z",
  "title": "Matrix integrals and Hurwitz numbers",
  "authors": [
    "A. Yu. Orlov"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider multi-matrix models which may be viewed as integrals of products of tau functions of matrix argument. Sometimes such integrals are tau functions themselves. We consider models which generate Hurwitz numbers $H^{\\textsc{e},\\textsc{f}}$, where $\\textsc{e}$ is the Euler characteristic of the base surface and $\\textsc{f}$ is the number of branch points. We show that in case the integrands contains the product of $n > 2$ matrices the integral generates Hurwitz numbers with Euler characteristic $\\textsc{e}\\le 2$ and the number of branch points $\\textsc{f}\\le n+2$, both numbers $\\textsc{e}$ and $\\textsc{f}$ depend on $n$ and the order of the multipliers in the matrix product. The number $\\textsc{e}$ may be even or odd (respectively describes Riemann (and cerian Klein) or only Klein (non-orientable) base surface) depending on the presence of the BKP tau functions in the integrand.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-09T18:43:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "matrix integrals",
      "branch points",
      "euler characteristic",
      "integral generates hurwitz numbers",
      "base surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}