{
  "abstract": "We consider simple random walk on the sequential affine preferential attachment graphs with fixed parameters $m\\ge2$ and $δ\\ge0$. We prove the walk has total-variation cutoff, and for every fixed $\\varepsilon\\in(0,1)$, \\[ t_{\\mathrm{mix}}^{(n)}(\\varepsilon) =\\frac{\\log n}{νd} +O_{\\mathbb P}\\!\\left(\\sqrt{\\log n}\\right), \\] where $ν>0$ is the walk speed and $d>0$ is the entropy per level of harmonic measure on the Pólya--point tree, the local weak limit of the graph. Thus cutoff occurs at the entropic time. Entropic cutoff was previously established for a range of random graph models including configuration models under mild degree assumptions and on Erdős--Rényi random graphs for typical starting points. We extend the harmonic-measure approach to preferential attachment, accounting for its age-dependent structure and hubs of polynomial degree. The local weak limit, the Pólya--point tree, provides a more tractable setting for analyzing the walk. The proof combines regeneration estimates on the local limit tree, a quantitative graph--tree coupling on the mixing-time scale, and control of hub excursions. We show that shortly before the cutoff time its distribution is close in total variation distance to a measure with small $L^\\infty$ distance from stationarity. When $m\\ge2$, the spectral gap is bounded away from zero with high probability which completes the upper-bound coupling argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00717",
  "author_total": 2,
  "authors": [
    {
      "name": "Allan Sly"
    },
    {
      "name": "Seoyeon Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fsddsx2ez0thv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00717",
  "fulltext_url": null,
  "id": "fsddsx2ez0thv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00717",
  "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.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fsddsx2ez0thv.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00717"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Cutoff for Simple Random Walk on Preferential Attachment Graphs",
  "title_text": "Cutoff for Simple Random Walk on Preferential Attachment Graphs",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/fsddsx2ez0thv",
  "venue": "arXiv",
  "versions": []
}