{
  "abstract": "Let $X=(X_1,\\dots,X_n)\\in\\{0,1\\}^n$ have a multivariate totally positive ($\\mathrm{MTP}_2$) law. We prove that $$ \\sum_{i<j}\\mathbb{E}\\left[\\left|\\mathrm{Cov}(X_i,X_j \\mid X_{[n]\\setminus\\{i,j\\}})\\right|\\right] \\le n/2, $$ and more generally a weighted MaxCut inequality for the fully conditioned covariances. As an application, we confirm a conjecture of Allen and O'Donnell on correlation rounding for signed $\\mathrm{MTP}_2$ laws.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10474",
  "author_total": 1,
  "authors": [
    {
      "name": "Gleb Smirnov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3hfd2h162x0my.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10474",
  "fulltext_url": null,
  "id": "3hfd2h162x0my",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10474",
  "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.PR"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7212119989",
  "pdf_url": "https://arxiv.org/pdf/2609.10474",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3hfd2h162x0my.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:16Z",
      "native_id": "2609.10474",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10474"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "MaxCut for $\\mathrm{MTP}_2$ Covariances",
  "title_text": "MaxCut for MTP_2 Covariances",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:16Z",
  "url": "https://research.draconitic.com/paper/3hfd2h162x0my",
  "venue": "arXiv",
  "versions": []
}