{
  "abstract": "It is well known that the \\Lovasz-Theta function of a random graph $G(n,\\tfrac{1}{2})$ is $Θ(\\sqrt{n})$. More precisely, it is tightly concentrated in the interval \\( [\\sqrt{n},\\, 2\\sqrt{n}], \\) where the upper bound follows from an explicit dual witness for the associated semidefinite program. Numerical evidence and heuristic arguments suggest that the true value is $(1+o(1))\\sqrt{n}$. However, closing this gap has remained a longstanding challenge, resisting existing techniques even in light of recent progress on sharp algorithmic thresholds and non-asymptotic free probability. In this work, we resolve this question by proving that the \\Lovasz-Theta function of $G(n,\\tfrac{1}{2})$ is $(1+o_n(1))\\sqrt{n}$ with high probability, determining its asymptotic value up to vanishing relative error.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30064",
  "author_total": 2,
  "authors": [
    {
      "name": "Aaron Potechin"
    },
    {
      "name": "Jeff Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/20x5p1a97b54b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30064",
  "fulltext_url": null,
  "id": "20x5p1a97b54b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30064",
  "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.CC"
    ],
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
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  "openalex": "W7214363506",
  "pdf_url": "https://arxiv.org/pdf/2609.30064",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/20x5p1a97b54b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.30064",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30064"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sharp Lovasz-Theta Bounds on Random Graphs",
  "title_text": "Sharp Lovasz-Theta Bounds on Random Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/20x5p1a97b54b",
  "venue": "arXiv",
  "versions": []
}