{
  "abstract": "We show that the guaranties of the Gram-Schmidt Walk Algorithm of Bansal, Dadush, Garg, and Lovett can be achieved by an Ising model. Given vectors $v_1, \\ldots, v_n$ of norm less than 1, we give a closed form for a centrally symmetric distribution on a vector $σ\\in \\{\\pm 1 \\}^n$ so that the signed sum $\\sum_j σ(j) v_j$ is $1$-subgaussian. We show that the Glauber dynamics for this model mix rapidly provided that the norms of the input vectors are bounded below 1 by an inverse-polynomial. The proofs employ the theory of Lorentzian polynomials, and we use these techniques to show fast mixing bounds for other spin systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18639",
  "author_total": 3,
  "authors": [
    {
      "name": "Heng Guo"
    },
    {
      "name": "Daniel A. Spielman"
    },
    {
      "name": "Xinyuan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c9qfak4w6nm3p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18639",
  "fulltext_url": null,
  "id": "c9qfak4w6nm3p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18639",
  "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.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7221746740",
  "pdf_url": "https://arxiv.org/pdf/2610.18639",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c9qfak4w6nm3p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18639",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18639"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Subgaussian Vector Balancing by an Ising Model",
  "title_text": "Subgaussian Vector Balancing by an Ising Model",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:45Z",
  "url": "https://research.draconitic.com/paper/c9qfak4w6nm3p",
  "venue": "arXiv",
  "versions": []
}