{
  "abstract": "For every $α\\in(1/4,1)$, we construct a heterogeneous medium $ξ$ such that the diameter of the level sets of the solution to the F-KPP equation is of order $t^α$ along a sequence of times tending to infinity. This is a natural continuation of a series of recent works establishing logarithmic lower bounds as well as linear asymptotics for the diameters of the respective level sets in random and deterministic heterogeneous media. Both results assume $\\supξ> 2\\infξ$; we also show that the diameter can diverge in the critical regime $\\supξ=2\\infξ$. A key ingredient is an estimate for branching Brownian motion with fixed time horizon $t$ and branching rate $1$ on the negative half-line and $2+t^{-η}$ on the positive half-line. This estimate exhibits a saturation transition: for $η<1/2$ the polynomial and logarithmic corrections to the extremal position depend on $η$, whereas for $η\\geq1/2$ the extremal position becomes independent of $η$, up to an additive constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03332",
  "author_total": 3,
  "authors": [
    {
      "name": "Alexander Drewitz"
    },
    {
      "name": "Pascal Hanigk"
    },
    {
      "name": "Lisa Hartung"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8n1kay0vj224p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03332",
  "fulltext_url": null,
  "id": "8n1kay0vj224p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03332",
  "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.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03332",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8n1kay0vj224p.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03332",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03332"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Sublinear Power-Law Growth of Level Set Diameters in Heterogeneous F-KPP Equations",
  "title_text": "Sublinear Power-Law Growth of Level Set Diameters in Heterogeneous F-KPP Equations",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/8n1kay0vj224p",
  "venue": "arXiv",
  "versions": []
}