{
  "id": "math/0407260",
  "version": "v1",
  "published": "2004-07-15T00:47:52.000Z",
  "updated": "2004-07-15T00:47:52.000Z",
  "title": "On the shape of the ground state eigenfunction for stable processes",
  "authors": [
    "Rodrigo Banuelos",
    "Tadeusz Kulczycki",
    "Pedro J. Mendez-Hernandez"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that the ground state eigenfunction for symmetric stable processes of order $\\alpha\\in (0, 2)$ killed upon leaving the interval $(-1, 1)$ is concave on $(-{1/2}, {1/2})$. We call this property \"mid--concavity.\" A similar statement holds for rectangles in $\\R^d$, $d>1$. These result follow from similar results for finite dimensional distributions of Brownian motion and subordination.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-07-15T00:47:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ground state eigenfunction",
      "finite dimensional distributions",
      "similar statement holds",
      "similar results",
      "brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......7260B"
    }
  }
}