{
  "abstract": "We prove that the probability that Gaussian elimination with partial pivoting on $n \\times n$ random matrices has growth $ρ$ is at least inverse quasi-polynomial: $Ω(\\exp(-c \\log^2 (ρ)\\log(n)))$ for some constant $c > 0$. This lower bound breaks standard conjectures in the smoothed and average-case analysis of Gaussian elimination. To the best of our knowledge, it is the first non-trivial lower bound on the probability of large growth for Gaussian random matrices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08701",
  "author_total": 2,
  "authors": [
    {
      "name": "Daniel A. Spielman"
    },
    {
      "name": "Xifan Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8x8wcfy2h4mda.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08701",
  "fulltext_url": null,
  "id": "8x8wcfy2h4mda",
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  "landing_url": "https://arxiv.org/abs/2610.08701",
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  "licence_label": "arXiv licence",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DS"
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      "arxiv",
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      "1703|Matrix Theory and Algorithms"
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  "openalex": "W7220957172",
  "pdf_url": "https://arxiv.org/pdf/2610.08701",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8x8wcfy2h4mda.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08701",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08701"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Large Growth Happens: Gaussian Elimination with Partial Pivoting on Random Matrices",
  "title_text": "Large Growth Happens: Gaussian Elimination with Partial Pivoting on Random Matrices",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/8x8wcfy2h4mda",
  "venue": "arXiv",
  "versions": []
}