{
  "abstract": "In this note we first consider the Heisenberg uncertainty principle. We show that it acts as a {\\bf forcing mechanism} in the following sense. Real functions that approach its limit are close to Gaussian distributions, with proximity both in the sense of total variation distance and Wasserstein-1 distance. We next consider the uncertainty principle for functions defined on finite Abelian groups, and show that it acts as a forcing mechanism in the following sense. Functions that approach its limit are close (after translation and modulation by a complex exponential) to indicator functions of some subgroup, with proximity measured in ${\\mathbb {L}}^1$-norm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38909",
  "author_total": 1,
  "authors": [
    {
      "name": "Laurent Massoulié"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c6pc1hyxpdwc8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38909",
  "fulltext_url": null,
  "id": "c6pc1hyxpdwc8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38909",
  "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",
      "math.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38909",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c6pc1hyxpdwc8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38909",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38909"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uncertainty principles as forcing mechanisms",
  "title_text": "Uncertainty principles as forcing mechanisms",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/c6pc1hyxpdwc8",
  "venue": "arXiv",
  "versions": []
}