{
  "abstract": "We construct non-co-sofic invariant random subgroups in connected simple real Lie groups of rank one with finite center, in Zariski connected simple rank-one groups over non-Archimedean local fields, and in Aut(T) for regular and bi-regular trees T. This gives a negative answer to the continuous analogue of the classical Aldous-Lyons conjecture for these groups. Our constructions build on the existence of a finitely generated non-sofic group and answer a question raised in the author's ICM paper [Gel18].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08581",
  "author_total": 1,
  "authors": [
    {
      "name": "Tsachik Gelander"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/azbzmbx1bnwkb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08581",
  "fulltext_url": null,
  "id": "azbzmbx1bnwkb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08581",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7221033490",
  "pdf_url": "https://arxiv.org/pdf/2610.08581",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/azbzmbx1bnwkb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.08581",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08581"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Counterexamples to the continuous Aldous-Lyons conjecture",
  "title_text": "Counterexamples to the continuous Aldous-Lyons conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/azbzmbx1bnwkb",
  "venue": "arXiv",
  "versions": []
}