{
  "abstract": "We investigate rigidity phenomena in one-dimensional point processes. We show that the existence of an $L^1$ transport map from a stationary lattice or the Lebesgue measure to a point process is sufficient to guarantee the properties of Number-Rigidity and Cyclic-Factor. We then apply this result to non-singular Riesz gases with parameter $s\\in(-2,-1]$, defined in infinite volume as accumulation points of stationarized finite-volume Riesz gases. This includes, for $s=-1$, the well-known one-dimensional Coulomb gas (also called Jellium plasma, or the one-component 1D plasma).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2510.17257",
  "author_total": 2,
  "authors": [
    {
      "name": "David Dereudre"
    },
    {
      "name": "Rafaël Digneaux"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dmfvmh5y8c6qg.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "dmfvmh5y8c6qg",
  "issns": [],
  "landing_url": "https://hal.science/hal-05318149v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-pr"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05318149/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dmfvmh5y8c6qg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:34Z",
      "native_id": "hal-05318149",
      "source": "hal",
      "url": "https://hal.science/hal-05318149v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-pr",
      "subfield": "probability"
    }
  ],
  "title": "Rigidity of one-dimensional point processes via optimal transport",
  "title_text": "Rigidity of one-dimensional point processes via optimal transport",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:34Z",
  "url": "https://research.draconitic.com/paper/dmfvmh5y8c6qg",
  "venue": "HAL",
  "versions": []
}