{
  "abstract": "Cladograms of size $n$ are unrooted binary trees whose leaves are labelled from 1 to $n$. Aldous introduced in 2000 a Markov chain on cladograms, a step of which consists of removing a leaf uniformly at random and reinserting it on a uniformly chosen edge. We introduce a coupling for this walk, which follows multiple colored subtrees in parallel. We go around the lack of independence of the colored components by finding a relevant statistic, namely the sum of the squares of the sizes of all colored components, which we prove has a drift. We deduce that the mixing time of the walk is of order $n^2$, solving a conjecture of Aldous.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16955",
  "author_total": 2,
  "authors": [
    {
      "name": "Valentin Féray"
    },
    {
      "name": "Lucas Teyssier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5wqpsype2q837.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16955",
  "fulltext_url": null,
  "id": "5wqpsype2q837",
  "issns": [],
  "landing_url": "https://hal.science/hal-05772585v1",
  "language": "en",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7213429676",
  "pdf_url": "https://arxiv.org/pdf/2609.16955",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5wqpsype2q837.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:45Z",
      "native_id": "hal-05772585",
      "source": "hal",
      "url": "https://hal.science/hal-05772585v1"
    },
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16955",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16955"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Aldous chain on cladograms mixes in order $n^2$ steps",
  "title_text": "The Aldous chain on cladograms mixes in order n^2 steps",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/5wqpsype2q837",
  "venue": "HAL",
  "versions": []
}