{
  "id": "1609.01273",
  "version": "v1",
  "published": "2016-09-05T19:58:28.000Z",
  "updated": "2016-09-05T19:58:28.000Z",
  "title": "Lipschitz Embeddings of Random Fields",
  "authors": [
    "Riddhipratim Basu",
    "Vladas Sidoravicius",
    "Allan Sly"
  ],
  "comment": "48 pages, 13 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider the problem of embedding one i.i.d.\\ collection of Bernoulli random variables indexed by $\\mathbb{Z}^d$ into an independent copy in an injective $M$-Lipschitz manner. For the case $d=1$, it was shown by Basu and Sly (PTRF, 2014) to be possible almost surely for sufficiently large $M$. In this paper we provide a multi-scale argument extending this result to higher dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-05T19:58:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random fields",
      "lipschitz embeddings",
      "bernoulli random variables",
      "multi-scale argument",
      "higher dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}