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  "slug": "inclusion-link-chernoff-concentration",
  "title": "Chernoff concentration from inclusion-link spectral bounds",
  "shortTitle": "Concentration without independent choices",
  "url": "https://evidencepress.org/releases/inclusion-link-chernoff-concentration/",
  "oneLine": "A retained-set construction turns inclusion-link covariance control into scalar concentration, with a proposed mean-sensitive bound for variable-size samples.",
  "abstract": "This unrefereed analytic candidate derives a two-sided concentration inequality for additive statistics on fixed-size random sets from spectral bounds on every inclusion link. An extension assumes an inclusion-link covariance bound and obtains a negative-binomial moment-generating-function comparison and a mean-sensitive upper tail for arbitrary variable-size random sets, with a Poisson comparison at parameter one. The proof uses an attributed birth–death spectral-gap criterion and a retained-face construction that recovers original untilted inclusion laws. It does not claim matrix concentration, arbitrary Lipschitz concentration, a variable-rank lower tail or resolution of the separate TD-threshold question.",
  "datePublished": "2026-10-13",
  "dateModified": "2026-10-13",
  "version": "1.1.0-candidate",
  "doi": "10.5281/zenodo.23351344",
  "doiUrl": "https://doi.org/10.5281/zenodo.23351344",
  "conceptDoi": "10.5281/zenodo.23351343",
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  "authors": [
    "Anonymous"
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  "attributionBoundary": null,
  "problem": {
    "name": "Scalar lifted-vertex concentration from inclusion-link spectral bounds",
    "url": "https://arxiv.org/abs/2404.10961v2"
  },
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  "metadataProvenance": "Revised manuscript, exact-version archive and internal checks, 13 October 2026; provider availability is recorded separately.",
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  "keywords": [
    "concentration inequalities",
    "inclusion links",
    "spectral independence",
    "covariance bounds",
    "dependent sampling",
    "Chernoff bounds",
    "independent thinning"
  ],
  "keyResults": [
    "For rank d, link-walk bounds λ₂(P_A) ≤ η/r imply a two-sided additive concentration bound with exponent −ε²d/[4(1+η)].",
    "The proposed covariance-based extension gives a mean-sensitive upper tail for bounded additive statistics on variable-size random sets.",
    "A negative-binomial MGF comparison has a Poisson limit at covariance parameter one; it is not a distributional identity.",
    "The retained-face construction recovers original inclusion-link laws and uses an explicitly attributed auxiliary spectral-gap criterion."
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  "relatedWorks": [
    {
      "citation": "Dikstein and Hopkins, Chernoff Bounds and Reverse Hypercontractivity on HDX, arXiv:2404.10961v2. The scalar lifted-vertex spectral-independence branch is the motivating question; other branches remain separate.",
      "url": "https://arxiv.org/abs/2404.10961v2",
      "doi": "10.48550/arXiv.2404.10961"
    },
    {
      "citation": "Chen and coauthors, Rapid Mixing on Random Regular Graphs beyond Uniqueness, arXiv:2504.03406v2, Theorem 1.9 and Section 4.1. Attributed field-dynamics input.",
      "url": "https://arxiv.org/abs/2504.03406v2",
      "doi": "10.48550/arXiv.2504.03406"
    },
    {
      "citation": "Göbel and coauthors, A simple proof of rapid mixing on random regular graphs beyond uniqueness, arXiv:2606.27545v1, Theorem 1.2. Existing local matrix criterion specialized in the argument.",
      "url": "https://arxiv.org/abs/2606.27545v1",
      "doi": "10.48550/arXiv.2606.27545"
    },
    {
      "citation": "Kaufman, Kyng and Soldá, Scalar and Matrix Chernoff Bounds from ℓ∞ Independence, arXiv:2111.02177v2. Earlier one-sided-influence concentration, under a different hypothesis.",
      "url": "https://arxiv.org/abs/2111.02177v2",
      "doi": "10.48550/arXiv.2111.02177"
    },
    {
      "citation": "Anari and coauthors, Entropic Independence II, arXiv:2111.03247v1. Related concentration and restricted-field methods; arbitrary-field stability is not attributed to this work.",
      "url": "https://arxiv.org/abs/2111.03247v1",
      "doi": "10.48550/arXiv.2111.03247"
    },
    {
      "citation": "Blanca and coauthors, On mixing of Markov chains: Coupling, spectral independence, and entropy factorization, arXiv:2103.07459v1. Theorems 1.7 and 5.1 assume marginal boundedness.",
      "url": "https://arxiv.org/abs/2103.07459v1",
      "doi": "10.48550/arXiv.2103.07459"
    }
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