{
  "abstract": "We study the prevalence of hyperuniformity and spatial rigidity among translation- invariant ergodic simple point processes of fixed intensity, in a topology controlling local second moments. Hyperuniform processes are dense but meagre. We prove that intermittent hyperuniformity is residual: the number variance exhibits hyperuniform behavior along some sequences of radii and hyperfluctuating behavior along others. Maximal rigidity is also residual. Thus generic processes are maximally rigid but not hyperuniform. A local-to-global principle reduces the proofs to cross-section constructions for an arbitrary fixed essentially free ergodic $\\mathbb{R}^d$-action. We also prove that processes admitting revival sequences form a residual set and exhibit near-quadratic variance along suitable van Hove sequences.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01975",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael Björklund"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezvvjnzp53535.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01975",
  "fulltext_url": null,
  "id": "ezvvjnzp53535",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01975",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01975",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezvvjnzp53535.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01975",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01975"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Generic point processes are intermittently hyperuniform and maximally rigid",
  "title_text": "Generic point processes are intermittently hyperuniform and maximally rigid",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/ezvvjnzp53535",
  "venue": "arXiv",
  "versions": []
}