{
  "id": "1908.07287",
  "version": "v1",
  "published": "2019-08-20T12:00:32.000Z",
  "updated": "2019-08-20T12:00:32.000Z",
  "title": "Most Words are Geometrically Almost Uniform",
  "authors": [
    "Michael Larsen"
  ],
  "comment": "13 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "If w is a word in d>1 letters and G is a finite group, evaluation of w on a uniformly randomly chosen d-tuple in G gives a random variable with values in G, which may or may not be uniform. It is known that if G ranges over finite simple groups of given root system and characteristic, a positive proportion of words w give a distribution which approaches uniformity in the limit as |G| goes to infinity. In this paper, we show that the proportion is in fact 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-20T12:00:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G25",
      "14G15",
      "20G40"
    ],
    "keywords": [
      "finite simple groups",
      "finite group",
      "proportion",
      "root system",
      "uniformly randomly chosen d-tuple"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}