{
  "abstract": "Let $G$ be a finite simple $d$-regular graph, $d\\geq 3$, whose second largest adjacency eigenvalue satisfies $λ_2(G)\\leq (1-δ)d$, where $0<δ\\leq 1$. We prove that the Poincaré constant satisfies $$γ(G,\\|\\cdot\\|_X)\\lesssim \\frac{qCK}δ$$ whenever $X$ is a real Banach space with a $K$-unconditional Schauder basis and cotype $q$ with constant $C$. This constant compares the mean distance over all vertex pairs with the mean distance across edges. For real Banach lattices the bound is $O(qC/δ)$. The proof estimates where a random walk first leaves each coordinate level set. As a consequence of the bound, if $n$-vertex graphs in a fixed-degree expander family embed with bounded distortion into spaces with bounded $C,K$, then $q$ must grow at least as fast as $\\log n$. This order is attained in $\\ell_q^n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05649",
  "author_total": 1,
  "authors": [
    {
      "name": "Achintya Raya Polavarapu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8c402ts8c3bsf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05649",
  "fulltext_url": null,
  "id": "8c402ts8c3bsf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05649",
  "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.CO"
    ],
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05649",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8c402ts8c3bsf.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05649",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05649"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Linear Cotype Bounds for Nonlinear Spectral Gaps of Scalar Expanders",
  "title_text": "Linear Cotype Bounds for Nonlinear Spectral Gaps of Scalar Expanders",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:29Z",
  "url": "https://research.draconitic.com/paper/8c402ts8c3bsf",
  "venue": "arXiv",
  "versions": []
}