{
  "abstract": "Negative curvature makes the electrostatic Green function decay exponentially, producing a finite disorder-variance budget even as radial volume grows exponentially. We investigate whether this near-field concentration also determines wave-function participation on open hyperbolic lattices. A Gaussian control preserves the full one-site distribution of Comtet disorder at every vertex while removing its off-diagonal covariance. Complete-window participation ratios on $\\{7,3\\}$ graphs with $N=847,2240,5887$ yield an effective-exponent difference of $-0.028$ at $W/t=0.5$ and $+0.116$ at $W/t=3$; both signs persist upon extending to $N=15435$. Size-resolved squared-kernel radii lie near $2.45\\ell$ on the larger graphs of this sequence, below the cutoff-matched continuum value $3.12\\ell$. Distance-shell weights resolve the finite discrete measure associated with this shift, while higher participation moments and spacing ratios characterize the accompanying wave-function and spectral structure. A marginal-matched exponential-kernel family gives positive exponent contrasts at all five sampled kernel lengths at $W/t=0.5,3$, separating the Comtet response from a description based on the decay length alone. These results distinguish a concentrated variance budget from the covariance-dependent participation response of finite open hyperbolic systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01510",
  "author_total": 2,
  "authors": [
    {
      "name": "Wei Li"
    },
    {
      "name": "Yong Cheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/atscb27ejg7sk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01510",
  "fulltext_url": null,
  "id": "atscb27ejg7sk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01510",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.mes-hall"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01510",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/atscb27ejg7sk.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.01510",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01510"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Covariance-dependent participation scaling of Comtet disorder on open hyperbolic lattices",
  "title_text": "Covariance-dependent participation scaling of Comtet disorder on open hyperbolic lattices",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:18Z",
  "url": "https://research.draconitic.com/paper/atscb27ejg7sk",
  "venue": "arXiv",
  "versions": []
}