{
  "id": "2405.20571",
  "version": "v1",
  "published": "2024-05-31T01:53:04.000Z",
  "updated": "2024-05-31T01:53:04.000Z",
  "title": "On the principal eigenvalue for compound Poisson processes",
  "authors": [
    "Daesung Kim",
    "Hyunchul Park"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate the explicit expression for the principal eigenvalue $\\lambda_{1}^{X}(D)$ for a large class of compound Poisson processes $X$ on a bounded open set $D$ by examining its spectral heat content. When the jump density of the compound Poisson process is radially symmetric and strictly decreasing, we demonstrate that balls are the unique minimizers for $\\lambda_{1}^{X}(D)$ among all sets with equal Lebesgue measure. Furthermore, we show that this uniqueness fails if the jump density is not strictly decreasing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-31T01:53:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J76"
    ],
    "keywords": [
      "compound poisson process",
      "principal eigenvalue",
      "jump density",
      "spectral heat content",
      "equal lebesgue measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}