{
  "id": "2309.01263",
  "version": "v1",
  "published": "2023-09-03T20:03:13.000Z",
  "updated": "2023-09-03T20:03:13.000Z",
  "title": "$P$-log-Sobolev inequalities on $\\mathbb{N}$",
  "authors": [
    "Bartłomiej Polaczyk"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We answer an open problem posed by Mossel--Oleszkiewicz--Sen regarding relations between $p$-log-Sobolev inequalities for $p\\in(0,1]$. We show that for any interval $I\\subset(0,1]$, there exist $q,p\\in I$, $q<p$, and a measure $\\mu$ for which the $q$-log-Sobolev inequality holds, while the $p$-log-Sobolev inequality is violated. As a tool we develop certain necessary and closely related sufficient conditions characterizing those inequalities in the case of birth-death processes on $\\mathbb{N}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-03T20:03:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15"
    ],
    "keywords": [
      "log-sobolev inequality holds",
      "open problem",
      "mossel-oleszkiewicz-sen regarding relations",
      "birth-death processes",
      "closely related sufficient conditions characterizing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}