{
  "id": "2104.09980",
  "version": "v1",
  "published": "2021-04-20T14:07:20.000Z",
  "updated": "2021-04-20T14:07:20.000Z",
  "title": "Finite frames, frame potentials and determinantal point processes on the sphere",
  "authors": [
    "Masatake Hirao"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Herein, we address the expectations of frame potentials of three types of determinantal point processes(DPPs) on the d-dimensional unit sphere: (i) spherical ensembles on the 2-dimensional unit sphere; (ii) harmonic ensembles on the d-dimensional unit sphere and (iii) jittered sampling point processes on the d-dimensional unit sphere. The random point configurations generated by such DPPs converge more rapidly towards finite unit norm tight frames(FUNTFs) than the Poisson point processes on the unit sphere.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-20T14:07:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G55",
      "11K38"
    ],
    "keywords": [
      "determinantal point processes",
      "frame potentials",
      "d-dimensional unit sphere",
      "finite frames",
      "finite unit norm tight frames"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}