{
  "id": "1101.4454",
  "version": "v2",
  "published": "2011-01-24T06:55:39.000Z",
  "updated": "2013-06-12T01:10:38.000Z",
  "title": "Stein's method in high dimensions with applications",
  "authors": [
    "Adrian Röllin"
  ],
  "comment": "22 pages, published version",
  "journal": "Ann. Inst. H. Poincare Probab. Statist. 49 (2013), 529-549",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $h$ be a three times partially differentiable function on $R^n$, let $X=(X_1,\\dots,X_n)$ be a collection of real-valued random variables and let $Z=(Z_1,\\dots,Z_n)$ be a multivariate Gaussian vector. In this article, we develop Stein's method to give error bounds on the difference $E h(X) - E h(Z)$ in cases where the coordinates of $X$ are not necessarily independent, focusing on the high dimensional case $n\\to\\infty$. In order to express the dependency structure we use Stein couplings, which allows for a broad range of applications, such as classic occupancy, local dependence, Curie-Weiss model etc. We will also give applications to the Sherrington-Kirkpatrick model and last passage percolation on thin rectangles.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-12T01:10:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "steins method",
      "high dimensions",
      "applications",
      "high dimensional case",
      "multivariate gaussian vector"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013AnIHP..49..529R"
    }
  }
}