{
  "id": "2404.05503",
  "version": "v1",
  "published": "2024-04-08T13:25:13.000Z",
  "updated": "2024-04-08T13:25:13.000Z",
  "title": "Level-Set Percolation of Gaussian Random Fields on Complex Networks",
  "authors": [
    "Reimer Kuehn"
  ],
  "comment": "Main paper: 5 pages, 2 figures; supplementary material: 6 pages, 3 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We provide an explicit solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. The solution requires an analysis of the heterogeneous micro-structure of the percolation problem, i.e., a self-consistent determination of locally varying percolation probabilities. This is achieved using a cavity or message passing approach. It can be evaluated, both for single large instances of locally tree-like graphs, and in the thermodynamic limit of random graphs of finite mean degree in the configuration model class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-08T13:25:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian random fields",
      "complex networks",
      "level-set percolation",
      "single large instances",
      "finite mean degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}