{
  "abstract": "Let $G_N$ be a uniform random $d$-regular graph on $N$ vertices, with $d\\ge3$ fixed. Cooper and Frieze showed that the cover time of simple random walk on $G_N$ is asymptotically $θ_dN\\log N$, where $θ_d=(d-1)/(d-2)$. We prove that, in probability over the graph and uniformly in the starting point, $(T_{\\rm cov}-θ_dN\\log N)/(θ_dN)$ converges in distribution to a standard Gumbel law, confirming a prediction of Tishby, Biham, and Katzav [40]. The proof reduces late points to avoidance probabilities of finite sets via factorial moments, estimates these by Green-matrix capacities, and compares the latter with capacities on the infinite $d$-regular tree. We also obtain Gumbel limits for lazy, continuous-time and finitely many independent walks. For the unvisited set, we prove weighted laws of large numbers, spatial Poisson limits in the cover-time window, and joint Poisson limits for fixed tree-component shapes in their disappearance windows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26363",
  "author_total": 2,
  "authors": [
    {
      "name": "Lisa Hartung"
    },
    {
      "name": "Andreas Klippel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c1x05kjrdm9ps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26363",
  "fulltext_url": null,
  "id": "c1x05kjrdm9ps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26363",
  "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",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223007649",
  "pdf_url": "https://arxiv.org/pdf/2610.26363",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c1x05kjrdm9ps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26363",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26363"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Second-Order Cover Time of Random Regular Graphs",
  "title_text": "Second-Order Cover Time of Random Regular Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/c1x05kjrdm9ps",
  "venue": "arXiv",
  "versions": []
}