{
  "abstract": "We give a transfer principle for the fluctuations of linear statistics of finite particle systems around Lebesgue measure: if for a smooth kernel the variance decays polynomially with some exponent a compared to independent (non-interacting) particles, then the number variance over balls centred at almost every point decays with exponent min(1,a) times a log term if a=1, over a possibly reduced range of scales for non-periodic systems. We apply this principle to eigenvalues of random N*N Girko matrices, leveraging results of Cipolloni et al., and obtain the optimal perimeter-like number variance, on the microscopic and some mesoscopic scales range, after local averaging. We also apply the results to Coulomb gases, by transferring the results of Serfaty: we prove that 2D-Coulomb gases are 2-hyperuniform, i.e. they have surface order number variance, which is optimal, and that 3D Coulomb gases are 1-hyperuniform. In 2D, it allows to prove finite Coulomb energy and Wasserstein distance to Lebesgue measure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.22940",
  "author_total": 1,
  "authors": [
    {
      "name": "Raphaël Lachièze-Rey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/24tt31h9h4599.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.22940",
  "fulltext_url": null,
  "id": "24tt31h9h4599",
  "issns": [],
  "landing_url": "https://hal.science/hal-05663246v3",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
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      "hal",
      "0.math"
    ],
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      "hal",
      "1.math.math-pr"
    ],
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      "openalex",
      "2613|Random Matrices and Applications"
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  "openalex": "W7165614054",
  "pdf_url": "https://hal.science/hal-05663246/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/24tt31h9h4599.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:56Z",
      "native_id": "hal-05663246",
      "source": "hal",
      "url": "https://hal.science/hal-05663246v3"
    },
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2606.22940",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.22940"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "From smooth to discontinuous kernels: a variance transfer principle for hyperuniform processes",
  "title_text": "From smooth to discontinuous kernels: a variance transfer principle for hyperuniform processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/24tt31h9h4599",
  "venue": "HAL",
  "versions": []
}