{
  "abstract": "We establish marginal and functional convex order comparisons for graphon mean-field systems on $\\mathbb{R}^d$, including the infinite-horizon setting. A key difficulty is that convex order cannot in general be transferred through the usual particle approximation, which requires us to work directly with Euler schemes for the graphon mean-field system. Under a suitable dissipativity condition, we establish Euler approximation estimates that are uniform in both time and the agent label, and combine them with forward-backward induction arguments to obtain the convex order comparisons. For the infinite-horizon problem, dissipativity provides the required uniform-in-time stability, while an exponentially weighted $L^2$-space enables trajectory-level convergence and leads to the functional convex order on $[0,\\infty)$. As an application, we derive value-function comparisons for a class of one-dimensional linear-quadratic graphon mean-field games.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.19576",
  "author_total": 3,
  "authors": [
    {
      "name": "Daorong Cui"
    },
    {
      "name": "Shuoqing Deng"
    },
    {
      "name": "Yang Xiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bednhhjx448tc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.19576",
  "fulltext_url": null,
  "id": "bednhhjx448tc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.19576",
  "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.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7203862055",
  "pdf_url": "https://arxiv.org/pdf/2608.19576",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bednhhjx448tc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2608.19576",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.19576"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Convex ordering for graphon mean-field systems",
  "title_text": "Convex ordering for graphon mean-field systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/bednhhjx448tc",
  "venue": "arXiv",
  "versions": []
}