{
  "abstract": "The repeated averages process is a stochastic averaging process on graphs whose mixing time is known for several structured families, but no general sharp expression is known for all connected graphs. It was conjectured that the $L^2\\!\\to\\!L^1$ mixing time is of order $|E|\\log n/λ_2$. We disprove this conjecture using the graph $G_n$ obtained by attaching one leaf to the complete graph $K_n$. We prove that $λ_2(G_n)=1$ and that \\[ t_{\\varepsilon,2\\to1}(G_n)=Θ_{\\varepsilon}(γ(G_n))=Θ_{\\varepsilon}(n^2), \\] with no additional $\\log n$ factor. The example has a strongly localized Fiedler eigenvector: most of its squared $L^2$ mass lies on the leaf, while the balancing mass is spread across the clique.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21215",
  "author_total": 1,
  "authors": [
    {
      "name": "Nikash Gupta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d9dxgh97n2k1e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21215",
  "fulltext_url": null,
  "id": "d9dxgh97n2k1e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21215",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7213862097",
  "pdf_url": "https://arxiv.org/pdf/2609.21215",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d9dxgh97n2k1e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21215",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21215"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A counterexample to a mixing-time conjecture for repeated averages on graphs",
  "title_text": "A counterexample to a mixing-time conjecture for repeated averages on graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/d9dxgh97n2k1e",
  "venue": "arXiv",
  "versions": []
}