{
  "id": "1410.7354",
  "version": "v1",
  "published": "2014-10-27T19:03:17.000Z",
  "updated": "2014-10-27T19:03:17.000Z",
  "title": "The Mittag-Leffler process and a scaling limit for the block counting process of the Bolthausen-Sznitman coalescent",
  "authors": [
    "Martin Möhle"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The Mittag-Leffler process $X=(X_t)_{t\\ge 0}$ is introduced. This Markov process has the property that its marginal random variables $X_t$ are Mittag-Leffler distributed with parameter $e^{-t}$, $t\\in [0,\\infty)$, and the semigroup $(T_t)_{t\\ge 0}$ of $X$ satisfies $T_tf(x)={\\mathbb E}(f(x^{e^{-t}}X_t))$ for all $x\\ge 0$ and all bounded measurable functions $f:[0,\\infty)\\to{\\mathbb R}$. Further characteristics of the process $X$ are derived, for example an explicit formula for the joint moments of its finite dimensional distributions. The main result states that the block counting process of the Bolthausen-Sznitman $n$-coalescent, properly scaled, converges in the Skorohod topology to the Mittag-Leffler process $X$ as the sample size $n$ tends to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-27T19:03:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60J27",
      "92D15",
      "97K60"
    ],
    "keywords": [
      "block counting process",
      "mittag-leffler process",
      "bolthausen-sznitman coalescent",
      "scaling limit",
      "marginal random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.7354M"
    }
  }
}