{
  "abstract": "Let $\\mathcal H=(V,E)$ be a locally finite simple hypergraph, equip $V$ with the hyperpath metric, and consider the equal-edges random walk \\cite{CoupetteEtAl2023}. For adjacent vertices $x$ and $y$, we prove that the idleness function $α\\mapstoκ_α^{\\mathcal H}(x,y)$ is piecewise affine and with no more than three affine pieces. A separate mass-balance argument gives linearity on $[1/2,1]$ for every locally finite simple hypergraph and, consequently, a limit-free expression for the Lin--Lu--Yau curvature. In the $r$-uniform linear case, the hypergraph walk agrees exactly with the simple random walk on its 2-section. This reduction transfers the sharp endpoint intervals of Bourne, Cushing, Liu, Münch, and Peyerimhoff \\cite{BourneEtAl2018}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.01970",
  "author_total": 1,
  "authors": [
    {
      "name": "Qing Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/25fx9czwecbk4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.01970",
  "fulltext_url": null,
  "id": "25fx9czwecbk4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.01970",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7172442100",
  "pdf_url": "https://arxiv.org/pdf/2608.01970",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/25fx9czwecbk4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2608.01970",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.01970"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Idleness Functions for Ollivier-Ricci Curvature on Hypergraphs",
  "title_text": "Idleness Functions for Ollivier-Ricci Curvature on Hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/25fx9czwecbk4",
  "venue": "arXiv",
  "versions": []
}