{
  "abstract": "A right sub-gamma bound is described by a quadratic proxy $v$ and a pole $c$, and the pair is not unique: enlarging either preserves it. Fixing $v$ at the variance $V$ removes the ambiguity at quadratic order but is a convention, not a consequence. For centered infinitely divisible laws with finite nonzero variance we determine the entire boundary of the feasible set, the map $v\\mapsto c_*(v)$. A Beta$(1,2)$ multiplier applied to the normalised Kolmogorov canonical measure turns feasibility into a one-dimensional comparison and yields an exact variational formula: the frontier is convex, nonincreasing, and its feasible set is convex. The abscissa of convergence of the moment generating function imposes a $v$-insensitive floor on $c_*$, so a law whose variance-exact pole sits on it has a flat frontier, whereas the third-cumulant obstruction exists only at $v=V$. Whenever that pole lies strictly above both floors the frontier drops strictly as soon as $v>V$; if the control is also purely local with $κ_3^2/(9V^2)>κ_4/(12V)$, the drop has a square-root profile, and in the remaining boundary case a cube-root profile, with derivative $-\\infty$ at $V$ either way. We then characterise when the optimised frontier reproduces the exact Chernoff deviation: equality holds at a level exactly when some pair on the frontier is tangent to the cumulant generating function at a Legendre maximiser for that level. At the levels tabulated in a worked example $v=V$ costs four to thirty percent; for a centered exponential a gap persists at every level, reaching thirteen percent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23069",
  "author_total": 2,
  "authors": [
    {
      "name": "Yichuan Chen"
    },
    {
      "name": "Xin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f732y1frz9c8r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23069",
  "fulltext_url": null,
  "id": "f732y1frz9c8r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23069",
  "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.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7214004668",
  "pdf_url": "https://arxiv.org/pdf/2609.23069",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f732y1frz9c8r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23069",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23069"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Feasible Frontiers for Sub-Gamma Envelopes: the Variance--Pole Trade-off for Infinitely Divisible Laws",
  "title_text": "Feasible Frontiers for Sub-Gamma Envelopes: the Variance--Pole Trade-off for Infinitely Divisible Laws",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/f732y1frz9c8r",
  "venue": "arXiv",
  "versions": []
}