{
  "id": "1901.08390",
  "version": "v1",
  "published": "2019-01-24T13:10:17.000Z",
  "updated": "2019-01-24T13:10:17.000Z",
  "title": "Functional central limit theorems for multivariate Bessel processes in the freezing regime",
  "authors": [
    "Michael Voit",
    "Jeannette H. C. Woerner"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.CA",
    "math.MP"
  ],
  "abstract": "Multivariate Bessel processes $(X_{t,k})_{t\\ge0}$ describe interacting particle systems of Calogero-Moser-Sutherland type and are related with $\\beta$-Hermite and $\\beta$-Laguerre ensembles. They depend on a root system and a multiplicity $k$ which corresponds to the parameter $\\beta$ in random matrix theory. In the recent years, several limit theorems were derived for $k\\to\\infty$ with fixed $t>0$ and fixed starting point. Only recently, Andraus and Voit used the stochastic differential equations of $(X_{t,k})_{t\\ge0}$ to derive limit theorems for $k\\to\\infty$ with starting points of the form $\\sqrt k\\cdot x$ with $x$ in the interior of the corresponding Weyl chambers. Here we provide associated functional central limit theorems which are locally uniform in $t$. The Gaussian limiting processes admit explicit representations in terms of matrix exponentials and the solutions of the associated deterministic dynamical systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-24T13:10:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15",
      "60F05",
      "60J60",
      "60B20",
      "60H20",
      "70F10",
      "82C22",
      "33C67"
    ],
    "keywords": [
      "functional central limit theorems",
      "multivariate bessel processes",
      "processes admit explicit representations",
      "freezing regime",
      "limiting processes admit explicit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}