{
  "id": "2206.08276",
  "version": "v1",
  "published": "2022-06-16T16:16:41.000Z",
  "updated": "2022-06-16T16:16:41.000Z",
  "title": "Multiplicative structures and random walks in o-minimal groups",
  "authors": [
    "Hunter Spink"
  ],
  "comment": "20 pages, comments welcome!",
  "categories": [
    "math.LO",
    "math.CO",
    "math.PR"
  ],
  "abstract": "We prove structure theorems for o-minimal definable subsets $S\\subset G$ of definable groups containing large multiplicative structures, and show definable groups do not have bounded torsion arbitrarily close to the identity. As an application, for certain models of $n$-step random walks $X$ in $G$ we show upper bounds $\\mathbb{P}(X\\in S)\\le n^{-C}$ and a structure theorem for the steps of $X$ when $\\mathbb{P}(X\\in S)\\ge n^{-C'}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-16T16:16:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "o-minimal groups",
      "structure theorem",
      "groups containing large multiplicative structures",
      "step random walks",
      "definable groups containing large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}