{
  "id": "1908.11189",
  "version": "v1",
  "published": "2019-08-29T12:53:30.000Z",
  "updated": "2019-08-29T12:53:30.000Z",
  "title": "Some martingales associated with multivariate Bessel processes",
  "authors": [
    "Miklos Kornyik",
    "Michael Voit",
    "Jeannette H. C. Woerner"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.CA",
    "math.MP"
  ],
  "abstract": "We study Bessel processes on Weyl chambers of types A and B on $\\mathbb R^N$. Using elementary symmetric functions, we present several space-time-harmonic functions and thus martingales for these processes $(X_t)_{t\\ge0}$ which are independent from one parameter of these processes. As a consequence, $p(y):=\\mathbb E(\\prod_{i=1}^N (y-X_t^i))$ can be expressed via classical orthogonal polynomials. Such formulas on characteristic polynomials admit interpretations in random matrix theory where they are partially known by Diaconis, Forrester, and Gamburd.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-29T12:53:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15",
      "60F05",
      "60J60",
      "60B20",
      "60H20",
      "70F10",
      "82C22",
      "33C67"
    ],
    "keywords": [
      "multivariate bessel processes",
      "martingales",
      "characteristic polynomials admit interpretations",
      "random matrix theory",
      "study bessel processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}