{
  "abstract": "This article is concerned with the asymptotic shape of quantile surfaces, defined as the set of quantiles at a given level $α$ generated by a controlled one-dimensional distribution. Specifically, when the distribution arises as a linear combination of log-normal random variables and the control is a vector of positive coefficients, we prove that quantile surfaces are globally concave in the left tail ($α\\to0$) and globally convex in the right tail ($α\\to1$). Moreover, these surfaces exhibit asymptotic separation of scale and shape.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31345",
  "author_total": 2,
  "authors": [
    {
      "name": "Florian Gach"
    },
    {
      "name": "Simon Hochgerner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ej04baa4x6x2b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31345",
  "fulltext_url": null,
  "id": "ej04baa4x6x2b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31345",
  "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.PR"
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      "openalex",
      "2604|Point processes and geometric inequalities"
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  "openalex": "W7214580142",
  "pdf_url": "https://arxiv.org/pdf/2609.31345",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ej04baa4x6x2b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2609.31345",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31345"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "On the asymptotic shape of quantile surfaces",
  "title_text": "On the asymptotic shape of quantile surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/ej04baa4x6x2b",
  "venue": "arXiv",
  "versions": []
}