{
  "abstract": "We study the mixing time of two local Markov chains for uniformly sampling proper edge colorings of trees. For a tree with $n$ vertices and maximum degree $Δ$, we establish optimal mixing-time bounds for the single-edge Glauber dynamics when $q\\geΔ+2$ and for the neighboring-edge heat-bath dynamics when $q\\geΔ+1$. Both chains mix in $O_Δ(n(\\log n+\\log(1/\\varepsilon)))$ steps, uniformly over the number of colors $q$. These bounds are tight in their dependence on $n$ for fixed $Δ$. Our proof establishes log-Sobolev inequalities through local color release, reusable recoloring buffers, and component entropy mixing. The two dynamics require different local constructions: a two-spare-color buffer for single-edge updates and a second-layer controller for neighboring-edge updates. The resulting entropy analysis applies to general bounded-degree trees, including regimes where worst-case spatial mixing fails.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30625",
  "author_total": 1,
  "authors": [
    {
      "name": "Haoran wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cn39evtwp1em7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30625",
  "fulltext_url": null,
  "id": "cn39evtwp1em7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30625",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7223300476",
  "pdf_url": "https://arxiv.org/pdf/2610.30625",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cn39evtwp1em7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30625",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30625"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Optimal Mixing for Local Edge-Coloring Dynamics on Trees",
  "title_text": "Optimal Mixing for Local Edge-Coloring Dynamics on Trees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/cn39evtwp1em7",
  "venue": "arXiv",
  "versions": []
}