{
  "abstract": "We study the homogeneous Kuramoto model on random 3-regular graphs. A connected graph $G$ is globally synchronizing if, for almost every initial condition, the gradient flow converges to a fully synchronized state, in which all phases coincide. It has been conjectured by Bandeira [Oberwolfach Rep. 21 (2024) 1163-1226] that a random 3-regular graph $G_{2n,3}$ is globally synchronizing with high probability. We disprove this conjecture in a strong way: $G_{2n,3}$ is not globally synchronizing with probability tending to 1.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09135",
  "author_total": 3,
  "authors": [
    {
      "name": "Ciro Carvallo"
    },
    {
      "name": "Pablo Groisman"
    },
    {
      "name": "Dieter Mitsche"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/93hg4em1nhhzm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09135",
  "fulltext_url": null,
  "id": "93hg4em1nhhzm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09135",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1705|Nonlinear Dynamics and Pattern Formation"
    ]
  ],
  "openalex": "W7220940511",
  "pdf_url": "https://arxiv.org/pdf/2610.09135",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/93hg4em1nhhzm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.09135",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09135"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Random $3$-regular graphs are not globally synchronizing",
  "title_text": "Random $3$-regular graphs are not globally synchronizing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/93hg4em1nhhzm",
  "venue": "arXiv",
  "versions": []
}