{
  "id": "1610.05221",
  "version": "v1",
  "published": "2016-10-17T17:27:33.000Z",
  "updated": "2016-10-17T17:27:33.000Z",
  "title": "Balancing sums of random vectors",
  "authors": [
    "Juhan Aru",
    "Bhargav Narayanan",
    "Alex Scott",
    "Ramarathnam Venkatesan"
  ],
  "comment": "21 pages, submitted",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "We study a higher-dimensional 'balls-into-bins' problem. An infinite sequence of i.i.d. random vectors is revealed to us one vector at a time, and we are required to partition these vectors into a fixed number of bins in such a way as to keep the sums of the vectors in the different bins close together; how close can we keep these sums almost surely? This question, our primary focus in this paper, is closely related to the classical problem of partitioning a sequence of vectors into balanced subsequences, in addition to having applications to some problems in computer science.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-17T17:27:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60D05",
      "60C05"
    ],
    "keywords": [
      "random vectors",
      "balancing sums",
      "infinite sequence",
      "higher-dimensional balls-into-bins",
      "bins close"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}