{
  "id": "1609.08582",
  "version": "v1",
  "published": "2016-09-27T19:06:52.000Z",
  "updated": "2016-09-27T19:06:52.000Z",
  "title": "The two-dimensional Coulomb plasma: quasi-free approximation and central limit theorem",
  "authors": [
    "Roland Bauerschmidt",
    "Paul Bourgade",
    "Miika Nikula",
    "Horng-Tzer Yau"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For the two-dimensional one-component Coulomb plasma, we derive an asymptotic expansion of the free energy up to order $N$, the number of particles of the gas, with an effective error bound $N^{1-\\kappa}$ for some constant $\\kappa > 0$. This expansion is based on approximating the Coulomb gas by a quasi-free Yukawa gas. Further, we prove that the fluctuations of the linear statistics are given by a Gaussian free field at any positive temperature. Our proof of this central limit theorem uses a loop equation for the Coulomb gas, the free energy asymptotics, and rigidity bounds on the local density fluctuations of the Coulomb gas, which we obtained in a previous paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-27T19:06:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central limit theorem",
      "two-dimensional coulomb plasma",
      "quasi-free approximation",
      "coulomb gas",
      "two-dimensional one-component coulomb plasma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}