{
  "abstract": "We show that random tuples of matrices over a finite field are uniform dimension expanders for every expansion coefficient below the optimal one, using elementary counting arguments. The same holds for the optimal coefficient along a set of dimensions of density 1. By contrast, along Fibonacci dimensions random pairs of matrices fail to be optimal dimension expanders with probability bounded away from zero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32394",
  "author_total": 2,
  "authors": [
    {
      "name": "Urban Jezernik"
    },
    {
      "name": "Markus Reineke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/162erryncs80w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32394",
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  "id": "162erryncs80w",
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  "landing_url": "https://arxiv.org/abs/2610.32394",
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  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "native_subjects": [
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  "pdf_url": "https://arxiv.org/pdf/2610.32394",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/162erryncs80w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32394",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32394"
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  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
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  ],
  "title": "Optimality of finite field dimension expanders",
  "title_text": "Optimality of finite field dimension expanders",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/162erryncs80w",
  "venue": "arXiv",
  "versions": []
}