{
  "id": "1501.03963",
  "version": "v1",
  "published": "2015-01-16T12:19:25.000Z",
  "updated": "2015-01-16T12:19:25.000Z",
  "title": "A Spectral decomposition for the Bolthausen-Sznitman coalescent and the Kingman coalescent",
  "authors": [
    "Jonas Kukla",
    "Helmut H. Pitters"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider both the Bolthausen-Sznitman and the Kingman coalescent restricted to the partitions of $\\{1, \\ldots, n\\}.$ Spectral decompositions of the corresponding generators are derived. As an application we obtain a formula for the Green's functions and a short derivation of the well-known formula for the transition probabilities of the Bolthausen-Sznitman coalescent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-16T12:19:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "60J28",
      "92D25"
    ],
    "keywords": [
      "bolthausen-sznitman coalescent",
      "spectral decomposition",
      "greens functions",
      "short derivation",
      "well-known formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150103963K"
    }
  }
}