{
  "abstract": "We study the operator-norm approximation of Markov operators associated with finite graph coverings. Let $q:Y\\to X$ be a connected covering of degree $d\\geq 2$ between finite connected graphs, and let $A_q:C(Y)\\to C(X)$ be its fiber-averaging operator. We show that $A_q$ is not a finite convex combination of extreme Markov operators, although such combinations approximate $A_q$ arbitrarily well in operator norm. We determine the exact distances from $A_q$ to convex combinations of at most $m$ extreme Markov operators, with arbitrary or equal convex weights. If $m=kd+r$, where $k\\geq 0$ and $1\\leq r\\leq d$, these distances are $2(d-r+1)/[d(k(d-r+1)+1)]$ and $2r(d-r+1)/(dm)$, respectively. Both distances are attained and depend only on the covering degree $d$ and the number of terms $m$. We also determine when equal weights are optimal and quantify the additional approximation error when they are not. Our proofs use total-variation estimates and continuous rearrangements of labelled weighted atoms. In particular, the unrestricted errors have a common scaled limit, while the equal-weight errors exhibit residue-dependent asymptotic behavior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35575",
  "author_total": 3,
  "authors": [
    {
      "name": "Hülya Duru"
    },
    {
      "name": "Serkan İlter"
    },
    {
      "name": "Aygül Bilgin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e0vczs8h2353s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35575",
  "fulltext_url": null,
  "id": "e0vczs8h2353s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35575",
  "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.FA"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7223955735",
  "pdf_url": "https://arxiv.org/pdf/2610.35575",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e0vczs8h2353s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35575",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35575"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp Norm Approximation of Covering Markov Operators",
  "title_text": "Sharp Norm Approximation of Covering Markov Operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/e0vczs8h2353s",
  "venue": "arXiv",
  "versions": []
}