{
  "id": "2212.14484",
  "version": "v1",
  "published": "2022-12-29T23:41:58.000Z",
  "updated": "2022-12-29T23:41:58.000Z",
  "title": "Weak-disorder limit for directed polymers on critical hierarchical graphs with vertex disorder",
  "authors": [
    "Jeremy Clark",
    "Casey Lochridge"
  ],
  "comment": "26 pages, 4 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study models for a directed polymer in a random environment (DPRE) in which the polymer traverses a hierarchical diamond graph and the random environment is defined through random variables attached to the vertices. For these models, we prove a distributional limit theorem for the partition function in a limiting regime wherein the system grows as the coupling of the polymer to the random environment is appropriately attenuated. The sequence of diamond graphs is determined by a choice of a branching number $b\\in \\{2,3,\\ldots\\}$ and segmenting number $s\\in \\{2,3,\\ldots\\}$, and our focus is on the critical case of the model where $b=s$. This extends recent work in the critical case of analogous models with disorder variables placed at the edges of the graphs rather than the vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-29T23:41:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17",
      "82D60"
    ],
    "keywords": [
      "critical hierarchical graphs",
      "directed polymer",
      "weak-disorder limit",
      "vertex disorder",
      "random environment"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}