{
  "abstract": "Given a discrete countable group $Γ$, we introduce the concept of random subalgebras of the reduced group $C^*$-algebra $C_r^*(Γ)$. This extends the existing theory of invariant random subgroups and the one of invariant random subalgebras of the group von Neumann algebra ${\\rm L}(Γ)$. As applications, we provide a characterisation of $C^*$-simplicity, a condition for amenability of the group and show the existence and uniqueness of a maximal nuclear $Γ$-invariant unital $C^*$-subalgebra of $C^*_r(Γ)$. Moreover, we give a topological characterisation of exactness of any separable unital $C^*$-algebra. Finally, we study exotic random subalgebras of $C^*_r(Γ)$ and super-exotic random subalgebras of ${\\rm L}(Γ)$, that is, random subalgebras which do not arise purely from random subgroups of $Γ$ and not from random subalgebras of $C^*_r(Γ)$, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28295",
  "author_total": 3,
  "authors": [
    {
      "name": "Pierre Fima"
    },
    {
      "name": "Hanna Oppelmayer"
    },
    {
      "name": "Leyan Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e95qa382xktff.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28295",
  "fulltext_url": null,
  "id": "e95qa382xktff",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28295",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7223157317",
  "pdf_url": "https://arxiv.org/pdf/2610.28295",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e95qa382xktff.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28295",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28295"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Random $C^*$-subalgebras",
  "title_text": "Random C^*-subalgebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/e95qa382xktff",
  "venue": "arXiv",
  "versions": []
}