{
  "id": "1108.5011",
  "version": "v3",
  "published": "2011-08-25T05:38:47.000Z",
  "updated": "2015-09-13T15:07:13.000Z",
  "title": "Gaussian behavior on hyperplanes",
  "authors": [
    "Daniel Fresen"
  ],
  "comment": "28 pages",
  "categories": [
    "math.PR",
    "math.FA",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We observe that the function $\\Lambda _{n}:\\mathbb{R}^{n}\\rightarrow (0,\\infty )$ defined by \\begin{equation*} \\Lambda _{n}(x)=\\exp \\left( x_{1}-\\pi \\sum_{i=2}^{n}x_{i}^{2}\\right) \\end{equation*} appears in the tails of a large class of functions, with properties involving log-concavity, independence, and homogeneity, as well as the gamma function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-29T05:21:43.000Z",
      "title": "Central limit theorems for non-central sections of log-concave product measures and star shaped functions",
      "abstract": "A section of a function f defined on Euclidean space is the restriction of f to an affine subspace. We study functions with various regularity properties including independence, convexity and smoothness, and show that sections of these functions far from the origin approximate the normal density function. As a consequence, if X and Y are i.i.d. random variables with mild assumptions on their distribution, then the distribution of X+2Y conditional on the event that X+Y is large, is approximately normal.",
      "comment": "9 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-09-13T15:07:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F05",
      "60D05",
      "26B25",
      "26B35"
    ],
    "keywords": [
      "central limit theorems",
      "log-concave product measures",
      "star shaped functions",
      "non-central sections",
      "normal density function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.5011F"
    }
  }
}