{
  "id": "1605.03401",
  "version": "v1",
  "published": "2016-05-11T12:30:50.000Z",
  "updated": "2016-05-11T12:30:50.000Z",
  "title": "A $N$-branching random walk with random selection",
  "authors": [
    "Aser Cortines",
    "Bastien Mallein"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider an exactly solvable model of branching random walk with random selection, describing the evolution of a fixed number $N$ of individuals in the real line. At each time step $t\\to t\\!+\\!1$, the individuals reproduce independently at random making children around their positions and the $N$ individuals that form the $(t+1)$th generation are chosen at random among these children according to the Gibbs measure at temperature $\\beta$. We compute the asymptotic speed and the genealogical behaviour of the system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-11T12:30:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60K35"
    ],
    "keywords": [
      "branching random walk",
      "random selection",
      "time step",
      "gibbs measure",
      "individuals reproduce"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}