{
  "abstract": "We study the quantity $\\sup_{ϕ\\inΦ}\\limsup_{n\\to\\infty}ϕ(F_n)/|F_n|$, where $\\mathcal F= (F_n)_{n\\in\\mathbb{N}}$ is a sequence of finite subsets of a countable amenable group, and $Φ$ is a collection of subadditive functions. Under mild conditions on $Φ$ we prove that the aforementioned quantity equals the supremum over $ϕ\\inΦ$ of the limit of $ϕ(F)/|F|$ as $F$ becomes more and more invariant, multiplied by a ``Følnerness'' constant $C(\\mathcal F)\\in[1,\\infty]$. We have $C(\\mathcal F)=1$ if and only if $\\mathcal F$ is Følner. A corollary of this result is that every choice of a non-Følner sequence overestimates topological and measure-theoretic entropy by the multiplicative factor $C(\\mathcal F)$ (in the positive entropy case). We obtain a generalization of classical results of Goodman, Krug, and Newton, on the so-called proportionality principle for sequence entropy, and their extension by Gao, Huang, and Zhu to countable amenable groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08408",
  "author_total": 1,
  "authors": [
    {
      "name": "Nicanor Carrasco-Vargas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2t3shjbbx1fd8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08408",
  "fulltext_url": null,
  "id": "2t3shjbbx1fd8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08408",
  "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.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08408",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2t3shjbbx1fd8.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08408",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08408"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Averages of sub-additive functions through non-Følner sequences",
  "title_text": "Averages of sub-additive functions through non-Følner sequences",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/2t3shjbbx1fd8",
  "venue": "arXiv",
  "versions": []
}