{
  "id": "1804.06102",
  "version": "v1",
  "published": "2018-04-17T08:22:26.000Z",
  "updated": "2018-04-17T08:22:26.000Z",
  "title": "Max-linear models on infinte graphs generated by Bernoulli bond percolation",
  "authors": [
    "Claudia Klüppelberg",
    "Ercan Sönmez"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs, and investigate their relations to classical percolation theory. We formulate results for the oriented square lattice graph $\\mathbb{Z}^2$ and nearest neighbor bond percolation. Focus is on the dependence introduced by this graph into the max-linear model. As a natural application we consider communication networks, in particular, the distribution of extreme opinions in social networks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-17T08:22:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G70",
      "60K35"
    ],
    "keywords": [
      "bernoulli bond percolation",
      "max-linear model",
      "infinte graphs",
      "nearest neighbor bond percolation",
      "finite directed acyclic graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}