{
  "id": "1502.04796",
  "version": "v1",
  "published": "2015-02-17T04:58:02.000Z",
  "updated": "2015-02-17T04:58:02.000Z",
  "title": "An Inequality for Gaussians on Lattices",
  "authors": [
    "Oded Regev",
    "Noah Stephens-Davidowitz"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that for any lattice $L \\subseteq R^n$ and vectors $x, y \\in R^n$, \\[ \\rho(L+ x)^2 \\rho(L + y)^2 \\leq \\rho(L)^2 \\rho(L + x+y) \\rho(L + x - y) \\;, \\] where $\\rho$ is the Gaussian measure $\\rho(A) := \\sum_{w \\in A} e^{-\\pi ||w||^2}$. We show a number of applications, including bounds on the moments of the discrete Gaussian distribution, various monotonicity properties, and a positive correlation inequality for Gaussian measures on lattices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-17T04:58:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gaussian measure",
      "discrete gaussian distribution",
      "monotonicity properties",
      "positive correlation inequality",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150204796R"
    }
  }
}