{
  "id": "1603.09373",
  "version": "v1",
  "published": "2016-03-30T20:44:43.000Z",
  "updated": "2016-03-30T20:44:43.000Z",
  "title": "Dynamical invariance for random matrices",
  "authors": [
    "Jeremie Unterberger"
  ],
  "comment": "47 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a general Langevin dynamics for the one-dimensional N-particle Coulomb gas with confining potential $V$ at temperature $\\beta$. These dynamics describe for $\\beta=2$ the time evolution of the eigenvalues of $N\\times N$ random Hermitian matrices. The equilibrium partition function -- equal to the normalization constant of the Laughlin wave function in fractional quantum Hall effect -- is known to satisfy an infinite number of constraints called Virasoro or loop constraints. We introduce here a dynamical generating function on the space of random trajectories which satisfies a large class of constraints of geometric origin. We focus in this article on a subclass induced by the invariance under the Schr\\\"odinger-Virasoro algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-30T20:44:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B20",
      "60J60",
      "82C21"
    ],
    "keywords": [
      "random matrices",
      "dynamical invariance",
      "fractional quantum hall effect",
      "one-dimensional n-particle coulomb gas",
      "equilibrium partition function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160309373U",
      "inspire": 1439794
    }
  }
}