{
  "id": "1910.06835",
  "version": "v1",
  "published": "2019-10-15T14:48:29.000Z",
  "updated": "2019-10-15T14:48:29.000Z",
  "title": "Dirichlet-Poincaré profiles of graphs and groups",
  "authors": [
    "David Hume"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We define Poincar\\'{e} profiles of Dirichlet type for graphs of bounded degree, in analogy with the Poincar\\'{e} profiles (of Neumann type) defined in [HMT19]. The obvious first definition yields nothing of interest, but an alternative definition yields a spectrum of profiles which are quasi-isometry invariants and monotone with respect to subgroup inclusion. Moreover, in the extremal cases $p=1$ and $p=\\infty$, they detect the F\\o lner function and the growth function respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-15T14:48:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F69"
    ],
    "keywords": [
      "obvious first definition yields",
      "extremal cases",
      "subgroup inclusion",
      "quasi-isometry invariants",
      "alternative definition yields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}