{
  "id": "2408.05611",
  "version": "v1",
  "published": "2024-08-10T18:33:01.000Z",
  "updated": "2024-08-10T18:33:01.000Z",
  "title": "Mixing on Generalized Associahedra",
  "authors": [
    "William Chang",
    "Colin Defant",
    "Daniel Frishberg"
  ],
  "comment": "19 pages, 6 figures",
  "categories": [
    "math.CO",
    "cs.DS",
    "math.PR"
  ],
  "abstract": "Eppstein and Frishberg recently proved that the mixing time for the simple random walk on the $1$-skeleton of the associahedron is $O(n^3\\log^3 n)$. We obtain similar rapid mixing results for the simple random walks on the $1$-skeleta of the type-$B$ and type-$D$ associahedra. We adapt Eppstein and Frishberg's technique to obtain the same bound of $O(n^3\\log^3 n)$ in type $B$ and a bound of $O(n^{13} \\log^2 n)$ in type $D$; in the process, we establish an expansion bound that is tight up to logarithmic factors in type $B$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-10T18:33:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "associahedron",
      "generalized associahedra",
      "simple random walk",
      "similar rapid mixing results",
      "adapt eppstein"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}