{
  "id": "1502.07390",
  "version": "v1",
  "published": "2015-02-25T22:36:01.000Z",
  "updated": "2015-02-25T22:36:01.000Z",
  "title": "Branching random walk with selection at critical rate",
  "authors": [
    "Bastien Mallein"
  ],
  "comment": "29 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a branching-selection particle system on the real line. In this model the total size of the population at time $n$ is limited by $e^{a n^{1/3}}$. At each step $n$, every individual dies while reproducing independently, making children around their current position according to i.i.d. point processes. Only the $e^{a(n+1)^{1/3}}$ rightmost children survive to form the $(n+1)^\\mathrm{th}$ generation. This process can be seen as a generalisation of the branching random walk with selection of the $N$ rightmost individuals at each time, introduced by Brunet and Derrida. We obtain the asymptotic behaviour of position of the extremal particles alive at time $n$ by coupling this process with a branching random walk with a killing boundary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-25T22:36:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60J80"
    ],
    "keywords": [
      "branching random walk",
      "critical rate",
      "branching-selection particle system",
      "current position",
      "real line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}