{
  "id": "1610.00021",
  "version": "v1",
  "published": "2016-09-30T20:13:17.000Z",
  "updated": "2016-09-30T20:13:17.000Z",
  "title": "Feller property of the multiplicative coalescent with linear deletion",
  "authors": [
    "Balazs Rath"
  ],
  "comment": "22 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We modify the definition of Aldous' multiplicative coalescent process and introduce the multiplicative coalescent with linear deletion (MCLD). A state of this process is a square-summable decreasing sequence of cluster sizes. Pairs of clusters merge with a rate equal to the product of their sizes and clusters are deleted with a rate linearly proportional to their size. We prove that the MCLD is a Feller process. This result is a key ingredient in the description of scaling limits of the evolution of component sizes of the mean field frozen percolation model and the so-called rigid representation of such scaling limits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-30T20:13:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiplicative coalescent",
      "linear deletion",
      "feller property",
      "mean field frozen percolation model",
      "scaling limits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}