{
  "abstract": "We prove that random groups in the Gromov density model (under a certain divisibility condition) have property (T) asymptotically almost surely for any density $d > \\frac{1}{4}$. This established $\\frac{1}{4}$ as the threshold for property (T), since it was shown by Ashcroft that they do not have property (T) for $d < \\frac{1}{4}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21255",
  "author_total": 1,
  "authors": [
    {
      "name": "Izhar Oppenheim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5cdqt9tafk7mh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21255",
  "fulltext_url": null,
  "id": "5cdqt9tafk7mh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21255",
  "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.GR"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7213891841",
  "pdf_url": "https://arxiv.org/pdf/2609.21255",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5cdqt9tafk7mh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21255",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21255"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Property (T) for random groups in the density model with $d > \\frac{1}{4}$",
  "title_text": "Property (T) for random groups in the density model with d > 1/4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/5cdqt9tafk7mh",
  "venue": "arXiv",
  "versions": []
}