{
  "id": "2410.13551",
  "version": "v1",
  "published": "2024-10-17T13:49:07.000Z",
  "updated": "2024-10-17T13:49:07.000Z",
  "title": "Wetting Transition on Trees I: Percolation With Clustering",
  "authors": [
    "Aser Cortines",
    "Itamar Harel",
    "Dmitry Ioffe",
    "Oren Louidor"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A new ``Percolation with Clustering'' (PWC) model is introduced, where (the probabilities of) site percolation configurations on the leaf set of a binary tree are rewarded exponentially according to a generic function, which measures the degree of clustering in the configuration. Conditions on such ``clustering function'' are given for the existence of a limiting free energy and a wetting transition, namely the existence of a non-trivial percolation parameter threshold above and only above which the set of ``dry'' (open) sites have an asymptotic density. Several examples of clustering functions are given and studied using the general theory. The results here will be used in a sequel paper to study the wetting transition for the discrete Gaussian free field on the tree subject to a hard wall constraint.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-17T13:49:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B41",
      "82B26",
      "82B05"
    ],
    "keywords": [
      "wetting transition",
      "discrete gaussian free field",
      "non-trivial percolation parameter threshold",
      "hard wall constraint",
      "site percolation configurations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}