{
  "abstract": "We prove that the independence sequence of every sufficiently large forest is unimodal. The result follows from establishing log-concavity on a central interval of the sequence, along with monotonicity of the initial and final segments. The main analytic step is a central limit theorem for the size of a random independent set sampled with the hard-core model, uniform over all forests and over an interval of positive fugacities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20961",
  "author_total": 5,
  "authors": [
    {
      "name": "Ethan X. Fang"
    },
    {
      "name": "Junwei Lu"
    },
    {
      "name": "Eran Nevo"
    },
    {
      "name": "Yuan Yao"
    },
    {
      "name": "Hailun Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/65mzdaks6jgnn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20961",
  "fulltext_url": null,
  "id": "65mzdaks6jgnn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20961",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213893202",
  "pdf_url": "https://arxiv.org/pdf/2609.20961",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/65mzdaks6jgnn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.20961",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20961"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Unimodality of Independence Polynomials for Sufficiently Large Forests",
  "title_text": "Unimodality of Independence Polynomials for Sufficiently Large Forests",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/65mzdaks6jgnn",
  "venue": "arXiv",
  "versions": []
}