{
  "id": "2210.08214",
  "version": "v1",
  "published": "2022-10-15T07:05:26.000Z",
  "updated": "2022-10-15T07:05:26.000Z",
  "title": "The affine ensemble: determinantal point processes associated with the ax+b group",
  "authors": [
    "Luis Daniel Abreu",
    "Peter Balazs",
    "Smiljana Jakšić"
  ],
  "comment": "15 pages; J. Math. Soc. Japan, in press",
  "categories": [
    "math.PR",
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C^+ associated with the ax+b (affine) group, depending on an admissible Hardy function {\\psi}. We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set {\\Omega} contained in C^+. As a special case one recovers the DPP related to the weighted Bergman kernel. When {\\psi} is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-15T07:05:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "determinantal point processes",
      "affine ensemble",
      "hyperbolic landau levels",
      "asymptotic behavior",
      "exact value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}