{
  "abstract": "In this paper, we prove a monotonicity principle for Beckner inequalities of the form \\[ \\frac{μ(f^2)-μ(f^p)^{2/p}}{2-p}\\leq C\\E(f,f), \\qquad f\\in\\D(\\E),\\quad 1\\le p\\le2, \\] where $\\E$ is a conservative symmetric Dirichlet form. If the inequality holds for every exponent $p$, it holds with the same constant $C$ for all $q\\in[1,p]$. This resolves an open question posed in Chapter~6 of Wang's monograph~\\cite{Wangbook}. We also study weak Beckner inequalities of the form \\[ Ψ_p(f)\\le β(r)\\E(f,f)+r\\,\\Osc(f)^2,\\qquad f\\in\\D(\\E),\\quad r>0, \\] where $β$ is a rate function. We show that the same monotonicity principle preserves the entire rate function. We further derive consequences for polynomial rates, semigroup contractivity, and concentration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21568",
  "author_total": 4,
  "authors": [
    {
      "name": "Qingbo Lei"
    },
    {
      "name": "Cheng Li"
    },
    {
      "name": "Bo Wu"
    },
    {
      "name": "Jiyang Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8jcnss6kj0ve6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21568",
  "fulltext_url": null,
  "id": "8jcnss6kj0ve6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21568",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213956424",
  "pdf_url": "https://arxiv.org/pdf/2609.21568",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8jcnss6kj0ve6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21568",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21568"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Monotonicity of Beckner Inequalities",
  "title_text": "Monotonicity of Beckner Inequalities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/8jcnss6kj0ve6",
  "venue": "arXiv",
  "versions": []
}