{
  "abstract": "We prove that the independence sequence of every sufficiently large forest is strictly barrier log-concave: whenever $i_{k+1}>i_k$, one has $i_k^2>i_{k-1}i_{k+1}$. Consequently, every common downward coefficient tilt is unimodal, with one order threshold valid simultaneously for all $0<t\\le1$. As an application, we prove that every sufficiently large well-covered tree has a strictly log-concave independence polynomial. More generally, the latter conclusion holds for well-covered forests with sufficiently large matching number. Every sufficiently large forest with a palindromic independence polynomial is also strictly log-concave, with its modes at the central ranks. The proof establishes local coefficient-curvature estimates uniformly over forests of unbounded maximum degree and over activities tending to zero. Combined with the fixed-density theorem of Fang, Lu, Nevo, Yao, and Zheng, these estimates complete the strict log-concavity interval down to rank one through $\\lfloor17α/25\\rfloor$; the terminal fraction is inherited. The classical decreasing tail then yields the barrier property. A cumulative-coefficient corona theorem transfers barrier log-concavity of the base forest to full strict log-concavity of its leaf corona.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22098",
  "author_total": 1,
  "authors": [
    {
      "name": "Vadim E. Levit"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/16c618v7c1ac7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22098",
  "fulltext_url": null,
  "id": "16c618v7c1ac7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22098",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.22098",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/16c618v7c1ac7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22098",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22098"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Barrier Log-Concavity of Large Forests",
  "title_text": "Barrier Log-Concavity of Large Forests",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/16c618v7c1ac7",
  "venue": "arXiv",
  "versions": []
}