{
  "id": "2211.14188",
  "version": "v1",
  "published": "2022-11-25T15:44:03.000Z",
  "updated": "2022-11-25T15:44:03.000Z",
  "title": "Spectral Gap Inequalities on Nilpotent Lie Groups in Infinite Dimensions",
  "authors": [
    "Esther Bou Dagher",
    "Yaozhong Qiu",
    "Boguslaw Zegarlinski",
    "Mengchun Zhang"
  ],
  "comment": "37 pages, 6 sections",
  "categories": [
    "math.FA",
    "math.PR"
  ],
  "abstract": "We develop a general framework for spectral gap inequalities for Gibbs measures on infinite dimensional spin spaces over nilpotent Lie groups in terms of weak U-bounds and weak single-site spectral gap inequalities. We then provide sufficient conditions on the local specification and give examples of measures constructed using the Kaplan norm and generalising a few results for the Carnot-Caratheodory distance on the Heisenberg group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-25T15:44:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B62",
      "26D10",
      "22E30",
      "60K35"
    ],
    "keywords": [
      "nilpotent lie groups",
      "infinite dimensions",
      "weak single-site spectral gap inequalities",
      "infinite dimensional spin spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}