{
  "id": "math/0402409",
  "version": "v1",
  "published": "2004-02-25T15:00:54.000Z",
  "updated": "2004-02-25T15:00:54.000Z",
  "title": "Martingales and character ratios",
  "authors": [
    "Jason Fulman"
  ],
  "comment": "22 pages",
  "categories": [
    "math.RT",
    "math.PR"
  ],
  "abstract": "Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the symmetric group on transpositions. A generalization of these results is given for Jack measure on partitions. We also give a probabilistic proof of a result of Burnside and Brauer on the decomposition of tensor products.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-25T15:00:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "character ratio",
      "martingales",
      "central limit theorem",
      "probabilistic proof",
      "finite groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2409F"
    }
  }
}