{
  "abstract": "We discover an exponent-dependent phase transition phenomenon for optimal hypercontractivity: for every prescribed $q_0>2$, there exists a reversible continuous-time Markov chain on three state space with normalized spectral gap whose $(2,q)$-optimal hypercontractivity time satisfies $$ \\text{$t_{\\mathrm{opt}}(2,q)=\\frac12\\log(q-1)$ if and only if $q\\ge q_0$},$$ whereas the strict inequality $t_{\\mathrm{opt}}(2,q)>\\frac12\\log(q-1)$ holds for $2<q<q_0$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15553",
  "author_total": 5,
  "authors": [
    {
      "name": "Jie Cao"
    },
    {
      "name": "Shilei Fan"
    },
    {
      "name": "Yong Han"
    },
    {
      "name": "Yanqi Qiu"
    },
    {
      "name": "Zipeng Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fm2k8reddmey4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15553",
  "fulltext_url": null,
  "id": "fm2k8reddmey4",
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  "landing_url": "https://arxiv.org/abs/2609.15553",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.FA"
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      "arxiv",
      "math.MP"
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      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7213327967",
  "pdf_url": "https://arxiv.org/pdf/2609.15553",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fm2k8reddmey4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.15553",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15553"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Phase transition in optimal hypercontractivity",
  "title_text": "Phase transition in optimal hypercontractivity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/fm2k8reddmey4",
  "venue": "arXiv",
  "versions": []
}