{
  "id": "2001.04972",
  "version": "v1",
  "published": "2020-01-14T18:58:16.000Z",
  "updated": "2020-01-14T18:58:16.000Z",
  "title": "Spectral upper bound for the torsion function of symmetric stable processes",
  "authors": [
    "Hugo Panzo"
  ],
  "comment": "14 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We use H. Vogt's (2019) upper bound on the product of the principal eigenvalue and $L^\\infty$ norm of the torsion function for Brownian motion killed upon exiting a domain in $\\mathbb{R}^d$ to derive an analogous bound for the symmetric stable processes. In particular, the bound captures the correct order of growth in the dimension $d$, improving upon the existing result of Giorgi and Smits (2010). Along the way, we prove a torsion analogue of Chen and Song's (2005) two-sided eigenvalue estimates for subordinate Brownian motion, which may be of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-14T18:58:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric stable processes",
      "spectral upper bound",
      "torsion function",
      "subordinate brownian motion",
      "principal eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}