{
  "id": "math/0507343",
  "version": "v3",
  "published": "2005-07-17T12:20:14.000Z",
  "updated": "2007-06-19T13:13:11.000Z",
  "title": "Limit shapes of multiplicative measures associated with coagulation-fragmentation processes and random combinatorial structures",
  "authors": [
    "Michael Erlihson",
    "Boris Granovsky"
  ],
  "comment": "40 pages. The paper was extended and reorganized following referee's suggestions. It will be published in Ann. Inst. H. Poincare",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, $a_k\\sim Ck^{p-1}, k\\to\\infty, p>0$,where $C$ is a positive constant. The measures considered are associated with reversible coagulation-fragmentation processes and certain combinatorial structures, known as assemblies. We prove the functional central limit theorem for the fluctuations of a scaled random partition from its limit shape. We demonstrate that when the component size passes beyond the threshold value, the independence of numbers of components transforms into their conditional independence. Among other things, the paper also discusses, in a general setting, the interplay between limit shapes, threshold and gelation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-06-19T13:13:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "82C22"
    ],
    "keywords": [
      "limit shape",
      "random combinatorial structures",
      "multiplicative measures",
      "functional central limit theorem",
      "reversible coagulation-fragmentation processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7343E"
    }
  }
}