{
  "abstract": "We construct infinite words $w$ whose complexity functions are quadratically bounded, but whose discrete derivatives are not linearly bounded, resolving a question of Cassaigne. Moreover, we construct infinite words of polynomially bounded complexity, and subshifts of quasi-linear complexity, whose discrete derivatives do not decay compared to their complexity functions, thus exhibiting a typical exponentially-growing behavior. As an application, we give the first examples of subshifts of polynomial complexity whose Rauzy graphs do not have Benjamini-Schramm limits. Finally, we realize (up to an inevitable linear error factor) every function satisfying the necessary conditions, as the complexity function of a minimal, uniquely ergodic, cube-free subshift, strengthening previous realization results in this direction, and derive consequences for the growth of simple algebras and just-infinite semigroups satisfying nontrivial laws.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08973",
  "author_total": 4,
  "authors": [
    {
      "name": "Be'eri Greenfeld"
    },
    {
      "name": "Paul-Henry Leemann"
    },
    {
      "name": "Carlos Gustavo Moreira"
    },
    {
      "name": "Efim Zelmanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6qp4psfhdt9t9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08973",
  "fulltext_url": null,
  "id": "6qp4psfhdt9t9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08973",
  "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.DS"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08973",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6qp4psfhdt9t9.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08973",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08973"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Polynomial complexity, random graphs, and strict ergodicity",
  "title_text": "Polynomial complexity, random graphs, and strict ergodicity",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/6qp4psfhdt9t9",
  "venue": "arXiv",
  "versions": []
}