{
  "abstract": "We elucidate the notion of \"reasonable functions\" in the context of Cohen--Lenstra heuristics. For a sequence $(x_i)_i$ of independent random variables valued in an infinite discrete probability space $(X,p)$, we investigate for what sets $S$ of functions on $X$ it is true that almost surely, for all $f\\in S$, the average of $f$ on the sequence is equal to its expected value. We show that if $p$ decays sufficiently quickly, as e.g. the Cohen--Lenstra distribution does, then $\\bigcup_{q>1}L^q(X)$ is such a set; while if $p$ decays sufficiently slowly, then not even $\\bigcap_{q<\\infty}L^q(X)$ has this property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29880",
  "author_total": 2,
  "authors": [
    {
      "name": "Alex Bartel"
    },
    {
      "name": "Adam Morgan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ce8p4wkb3ryw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29880",
  "fulltext_url": null,
  "id": "2ce8p4wkb3ryw",
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  "landing_url": "https://arxiv.org/abs/2610.29880",
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  "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.NT"
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      "math.PR"
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      "openalex",
      "2602|Analytic Number Theory Research"
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  "openalex": "W7223232120",
  "pdf_url": "https://arxiv.org/pdf/2610.29880",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ce8p4wkb3ryw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29880",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29880"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On the notion of reasonable functions in Cohen--Lenstra type heuristics",
  "title_text": "On the notion of reasonable functions in Cohen--Lenstra type heuristics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/2ce8p4wkb3ryw",
  "venue": "arXiv",
  "versions": []
}