{
  "abstract": "We prove that the size of a random independent set in every nonempty forest has variance strictly smaller than its mean at common activity $0<t\\le1$. A rooted quadratic reserve gives quantitative forms of this inequality. Mean matching transfers the bounds to fixed-weight canonical completion laws, and exact binomial moments prove strict log-concavity for every forest corona and every well-covered forest. The stronger factorial normalization $((m-j)!i_j)_{j=0}^m$ is strictly log-concave; we give explicit coefficient margins, terminal sharpness, one-less smoothing, and the exact universal three-index binomial ULC prefix. An exact attachment argument doubles the rooted reserve for every nontrivial unweighted tree. For a single marked root, a square reserve holds through $Θ=\\tfrac12e^{3-2W(1/e)}$ and for every positive mark at roots of degree at most four. A stronger reserve holds through mark $15/14$. These estimates yield marked clique, adjacent-pair, and repulsive two-piece variance bounds with fixed-weight canonical transfer. Finally, arbitrary positive site activities in $[3t/4,t]$ satisfy a uniform rooted reserve on every forest. This proves strict log-concavity for weighted forest coronas with compatible base marks. An explicit weighted-star obstruction shows why an unrestricted heterogeneous extension is impossible. Complete proofs are included, together with the required classical graph characterization and variance comparison.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41102",
  "author_total": 1,
  "authors": [
    {
      "name": "Vadim E. Levit"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4c00waxqnbrbr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41102",
  "fulltext_url": null,
  "id": "4c00waxqnbrbr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41102",
  "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.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4c00waxqnbrbr.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Variance Bounds and Strict Log-Concavity for Forest Coronas",
  "title_text": "Variance Bounds and Strict Log-Concavity for Forest Coronas",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/4c00waxqnbrbr",
  "venue": "arXiv",
  "versions": []
}