{
  "id": "2405.13756",
  "version": "v1",
  "published": "2024-05-22T15:39:19.000Z",
  "updated": "2024-05-22T15:39:19.000Z",
  "title": "Asymptotics of Weighted Reflectable Walks in $A_2$",
  "authors": [
    "Torin Greenwood",
    "Samuel Simon"
  ],
  "comment": "To appear in 2024 Analysis of Algorithms proceedings in the Leibniz International Proceedings in Informatics",
  "categories": [
    "math.CO"
  ],
  "abstract": "Lattice walks are used to model various physical phenomena. In particular, walks within Weyl chambers connect directly to representation theory via the Littelmann path model. We derive asymptotics for centrally weighted lattice walks within the Weyl chamber corresponding to $A_2$ by using tools from analytic combinatorics in several variables (ACSV). We find universality classes depending on the weights of the walks, in line with prior results on the weighted Gouyou-Beauchamps model. Along the way, we identify a type of singularity within a multivariate rational generating function that is not yet covered by the theory of ACSV. We conjecture asymptotics for this type of singularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-22T15:39:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "05A16"
    ],
    "keywords": [
      "weighted reflectable walks",
      "lattice walks",
      "multivariate rational generating function",
      "weyl chambers connect",
      "littelmann path model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}